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

Okay, sounds good. Hopefully it goes well.

Both relays test the same resistance? 107 Ohms? I assume relay 2 is still not being grounded by the ECM. Since we don't have a way to check the IMMO module for faults, we're running out of options here. We can go through and start checking ECM grounds and see if a ground is missing, but I would expect a code or other symptoms.
I'll label all the ECM grounds so you can check them.

The issue with the Immobilizer can be difficult to diagnose just by the security light, Under pattern 1-3 the light will go On for 2 seconds and then there will be a couple different things that can happen but possibly being missed, or it can appear to be fine but the IMMO module is not sending the correct message to the ECM to ground the relay. Even lower than normal voltage to the IMMO module can cause it to fault out. The ECM needs to receive a logic immobilizer code.
This is the diagram showing how the IMMO control unit and ECM interact. But I can't suggest you replace the ECM without knowing it's at fault, they are way too expensive to try a known good module. There are just way too many possibilities here.
If you had a higher end scan tool that could show the ECM is receiving the correct messages from the Immobilizer or not, that could show one or the other is at fault.

I've been going through service info for a long time today on your vehicle, and it should be setting codes if there is a relay fault causing the crank no start, It might be time to have a shop or possibly a mobile tech to come out and do a full system scan to see if there are any codes stored in other modules. At least to tell you what the issue is.
Diagrams 7, 8 are the Grounds for the ECM. You can back probe these with a regular test light attached to a 12v source and the light should not drop out while cranking, being grounded through the ECM connectors.
But I don't want to see you replace any very expensive modules and end up with the same problem.
I'm going to keep looking for any more info and tests you can do.
Go through the fuses one more time with the test light, make sure they have power on both sides, and no fuses look like they have burnt pins, possibly heat related.

Are both relays the same part number? I guess they would have to be different part numbers, I see a couple different ones here. But I really want to see this thing running again for you, since you've done so much testing so far. If it's finally determined that the ECM failed, I'd like to open it up for you and see if it actually burned up the transistor. I can solder in another chip. I work on electronics on the side, so it's always helpful to be able to see how these circuit boards actually failed. Plus, if its repairable Ill mail it back and you'll have a spare ECM.
And just now I received a message back from an instructor, he teaches technicians, and I messaged him because I wasn't liking the responses I was getting from others concerning this case, and I will post his response below (3rd). He is stating as long as there is a way to verify that the ECM is commanding the relay on, but it's not happening, the relay driver failed. Which is what I think happened as well.
Live ECM data would have a PID showing if the relay command was there, or OK. And that's what we need to verify somehow.

Okay, sounds like a plan, if the ECM is replaced it will need to be programmed anyway which is something they will need to do. There are always software updates as well. But tell them what happened, and what you have already checked. Hopefully this will save on some diag time and cost. They really just need to check the live data for the fuel pump relays command. And you can send the ECM to me and I'll open it up and check it out, just tell them you want to keep the old ECM.