Crank no start, fuel pump relay and or circuit not working?

Okay, looks like our replies got crossed there. 3.6 amps is pretty low for a fuel pump. You did all the tests correctly, one thing I would add, is when doing your resistance check from pin 3 of the relay socket and the ECM connector unplugged to pin 17, with both the relay out and the ECM unplugged, I would check from either pin 3 or 17, it doesn't matter, check for any continuity to Ground. This will verify the wire is not shorted to ground anywhere in between the relay location and the ECM. Your meter should read OL when measuring for resistance to any Ground.
With your voltage drop test, you didn't have any 2 second fuel pump prime, or control of the relay at all. And measuring 11.2v and 9.8v, that's how much voltage is being lost between your meter leads. Or the technical term is "potential" between the 2 leads.
I would expect the fuel pump to draw about 6 amps, even up to 10 amps on some higher-pressure systems. So that pump reading is concerning. I will see if I can find a spec on that, but it's a low reading. I think the fuel filter is in the tank with the pump, but I'll look that up as well. But check that circuit for any resistance to ground. And I'll get back with you.

Okay, that's good, looks like the circuit is intact. That pretty much leaves us with two possibilities, either the #2 relay just failed on its own and that took out the ECM. Or the fuel pump is struggling and overheated the relay causing it to fail.
Since we are not 100% sure on the pump here, and corroded connections can cause heat buildup, we need to check a few more things. It was a wise move the keep the battery on a maintainer during key on testing.

But the next part is going to be a pain. Getting access to the pump connector to check for voltage drop from the Fuse (17 15amp) that feeds the fuel pump through relay #2, all the way to the fuel pump, since you can access it without dropping the tank. This is the Fuse box under the dash so it shouldnt be too much of a stretch. I've added the aftermarket diagrams 1, 2, then the OEM 3, and the 4th is the connector at the Fuel pump itself.

Service info here is stating you need to remove the center console to get to the fuel pump access cover, because the cover is under the rear floor carpet, but you may be able to get to it without having to remove the entire center console, that's a lot of work here. I'm not sure if you have attempted to get to the pump yet, but I've added all the instructions to replace the pump, but for right now, we just need access to the fuel pump connector in diagram 6, so you can check for any voltage drop to the (pump pin 5) to Fuse 17.
And then also check for voltage drop on the pumps ground which is pin 4 to Ground, while you have it running. There needs to be current flowing for any voltage drop to occur.

But if there's not excessive voltage drop on the power feed or ground, you will have to check the fuel pump itself for signs of overheating. There could be issues with the connector at the pumps cover or in the tank as well. If you can't get to the cover by removing the rear carpet and need to the instructions for the center console to come out, Ill pull those up for you. YouTube may have a video for it as well, which ill check. It looks like a lot to pull that console out.

Id get your meter and leads set up first and then jump the relay and start the vehicle. Since we do have a few connectors in series with the pump.
If you go to a Honda dealership to get a relay, tell them how much the pump is drawing for current flow, and see what they say about it. Its definitely low to me, so this could all have been a domino effect leading to the relays failure. Sorry for the long post, I just don't want to see a new ECM fail in a couple months or less.

It's okay, take your time with testing, if you're not in a rush, I'm not, I have mobile calls to go on today, hence my slow responses sometimes. Your multimeter being in series with the pump will read up to 10-Amps max, and usually only for about 15 seconds, or whatever is says on the meter itself, they are all different. Some have a 10 Amp fuse inside for checking current draw. I know one of my multimeters has a warning on the current reading, I believe it's a 15 second current reading followed by a 15min cool down time, so it really just depends on what the meter says on it. If it has a good battery in it, I think it's most likely accurate, if you doubt that it is, you can buy an amp clamp, they're great to have, you can check all kinds of components with them. Just make sure the one you buy is not designed for home installations only, it has to be able to read DC current, I know a lot of the ones that Lowes for example sell, are for AC current. You could try Harbor Freight, they have quite a few decent tools for testing that are not overly expensive.

The amp clamps I use are very expensive, but that is because they are designed to work with my Pico scope setup, so I can watch the current or voltage waveforms. But you only need to know what the pump is drawing for current. It would take forever to explain using an oscilloscope. Do mention the current reading you got when at the dealership; I'd be interested in what they have to say on it. The vehicle has very high mileage, so it might need a fuel pump as well. I tend to see these types of situations a lot (because I work on a lot of very high mileage vehicles), but it's where one failed component will take out a couple other components. Which is what sounds like happened here.
This happens sometimes with 2 wire ignition coils as well, since it's just one wire for power and the other wire goes directly into the ECM/PCM, when the coil shorts out, it will send excessive current flow through the computer and burn out the transistor driver. I did post this case to other techs to see what they think about the pumps current, and I'll let you know what responses I get. Sometimes a Honda tech will chime in and give some good advice.
Chat soon.

Al

Okay, I received some responses to this case, now besides the negative comments that always come from some guys, one of them was willing to be reasonable. Now Im not sure I agree 100% on everything he stated, because components do short out and cause damage. But he seemed to think that if the relay shorted out, the ECM would have deactivated that circuit and set a code, which we didnt see happen. He suggested having you recheck for any power on the relay's pin 3 circuit with the ECM plugged in again. For whatever reason, no one seemed to really take into consideration the low resistance of the original relay, which really bothered me.

But to just verify what he was saying, using an automotive test light hooked to battery negative and the ECM connector plugged in and key On, see if relay pin 3 lights a test light at all. Doing this might set a code in the ECM, but thats ok for now. We just need to know if power is shorted to that wire in some other location.
The other thing he was suggesting was the Immobilizer was active and causing the ECM to prevent grounding the relay and activating it. So depending on the type of scan tool you have, a higher end scan tool will be able to look at live data in other modules in the vehicle. And in turn, look into the Security system module to see if there are any data PIDs indicating the security system is preventing the relay from activating. I think you would also see the security light staying on when trying to crank it over, but that also depends on if the immobilizer system was faulting or the key was bad, etc.

The first two diagrams below are for identifying an Immobilizer issue or being active by the security light flashes or lack of. I assume the Check engine light comes on at Key on, because you are able to start the vehicle with the relay jumped out.
The 3rd diagram is the Immobilizer Log Status, which you may or may not be able to look into, again depending on your scan tools capabilities. It will indicate if any faults are detected and log them, like any computer would normally do. "0" is none, and "1" would be a fault detected.
Since the Immobilizer uses the fuel pump control to prevent the vehicle from starting, we will humor them and check it. So if you get any of the Security lighting patterns 2-5 or the Security light does not come on at all.

He had mentioned the same thing about being absolutely sure about an ECM failure before replacing it, and I agree with that. And Im sure you tested the relays resistance correctly. When you opened that relay up, I assume it had a resistor inside. Most relays have either a diode or resistor inside the relay or in series with the power feed of the relay to help with the transient high voltage that occurs when the relay is deactivated.

But start here by checking with a test light for power on pin 3 with the relay out. I know we did a voltage drop test across the ECM and ground, but using a test light will show there is a solid power source shorted to ECM connector E pin 17. And that would cause the ECM driver for the relay to burn out. Im going to look into some of these symptom related procedures.

Go ahead and grab two new PGM FI relays and replace both of them with only Honda OEM parts from the dealership. And go from there. If it's still a no start condition, then go ahead with checking for any power on pin 3. That way we know at least both are functioning okay. It's possible the ECM is shutting down the #2 relay circuit if the new relays are low on resistance as well. Just thinking about this some more, I have never seen a Honda relay cause an ECM failure.

Okay, sounds good. Let's hope this is just a bunch of bad relays. The low fuel pump current sent me over thinking things a bit. Might still be an issue, but this vehicle has extremely high mileage. And they always seem to have more than one problem. Everything wears out eventually.

Okay, yes you did the tests correctly, you're getting substantially higher voltage now for the pump huh. I wonder if your multimeter battery is low. And the one thing that's odd is the voltage on the control side of the relay with it out.

So, unplug the ECM connector and recheck with the test light for voltage. This way the ECM is out of the equation. There might be a power wire shorted to the relays control wire to the ECM. Thats what we need to know next. If so, we'll need to track down that short.

Somethings you might see that can be deceiving, with the ECM connector unplugged, there may or may not be voltage on the control wire (pin 3). This depends on where that voltage is coming from. If its something related to the ECM connector being plugged in, the stray voltage may disappear during this test.

Ill bring up service info again and see what else is on connector E, but you've got you're testing down well, for sure. I'm glad to see that higher amperage from the pump. That really threw me off for a minute. But if that voltage is a shorted power wire, sending voltage down into the ECM on the relays control wire, that can potentially burn the ECM driver. Do that test and see if the test light doesn't light up anymore.
Was the test light really bright? I think you mentioned you were reading 11volts at some points on that wire. Sometimes a power short will only dimly light a test lamp.
This ECM has 5 connectors, correct?

Hook the test light to Battery negative (or any Ground but make sure the test light is grounded good by touching a power source) and with the ECM E connector plugged in (relay out) touch pin 3 with the tip of the test light, key off and then key On.
Sorry I should have been more specific about this.

We need to look for stray power on that wire. If it lights, then unplug the ECM connector E and retest the same. Not involving pin 5 at all.

We are looking for a short to power on the wire from pin 3 to the ECM connector here. Not a short to ground, you already verified that with your continuity test.
I apologize, I always have multiple things going on during the day.

Okay last test for today, and then try a couple new OEM Honda relays. Same test, just with the ECM connector E unplugged. Test light hooked to Ground and touching with the tip to pin 3 with key Off, and key On. That will verify there's nothing internal to the ECM that could be limiting current flow preventing the test light bulb from illuminating.

Pretty much after this, we will try the new relays with the correct resistance. If things don't improve we'll need to load test circuits. This is what I use for load testing (pic), it's a turn signal bulb with 2 filaments. One filament is 4 amps, and the other is about 1 amp.

To load test a circuit, (an ECM ground for example), the load test light will be hooked to battery positive, then I'll disconnect the ECM connector and use its Ground wire in the ECM connector to ground my load tester, if the lamp lights, I know that ground circuit can carry either the 4amps or the 1amp, depending on how much load I want to put on the wire.
At the same time, I will voltage drop that wire with the load on it, having the multimeter hooked in parallel with the load test light. So, if the test light does not light, I'll know what the voltage drop is on that ground wire.

The same can be done with a power feed, you just have to make sure you're not pulling those 4 amps through the module (ECM is this case). You're only going from its connector to power or ground source.
This test must always be done before condemning any modules. Along with any inputs or outputs checked to make sure there isnt something else causing the ECM to act strange, not activating components/circuits.

The reason for load testing power and ground feeds is that normal test lights only pull a few hundred milliamps and that is not enough to verify wire integrity. Even with a resistance test, there can be just one strain of wire left, and that will check out as zero ohms of resistance, but it will not carry enough current for the module to operate.
We will also need to load test the pin 3 to E17 wire. Although relays only pull about 200ma at most.

I assume when you turn the key On, the security light only comes on for 2 sec then goes out? I've had others suggest checking the Immobilizer or ECM live data for any data PIDs having to do with the security system. One was pretty sure this was an Immobilizer fault, but the scan tool you have can't access the security system module, so that is tricky part here. Since the circuit we are dealing with is the IMMO circuit.

I'll post a diagram for you showing exactly how to do this, because if you accidentally pull 4 amps through a module it will be damaged. Another long post today.

I think it's Security pattern 1 also, but I got 2 guys that insisted it was an IMMO issue, so we'll try two new relays and go from there. They seemed to disregard the fact that the relay was shorted out, I know some modules have protection from short circuits, but I've seen plenty of failures too.

Yes, try the 2 new relays first, let's see what happens. I'm not usually a parts changer, but in this case, we don't really know if this ECM will shut down a circuit like this in time to prevent damage. Plus, it did not set any codes, which if there was circuit protection like that, it should have. Try the relays even before making up a load test light, let's see if these other guys were right, clear any codes out before trying to start it if there are any set.