Code P0688?

Hello, we can post a wiring diagram for you on this, have you checked for power at the ASD relay location with the key on? I'll grab the wiring diagrams for you.

With the ASD Relay out, and key on you should have power (12v) on 2 of the relay's pins, just don't spread the pins where the relay lives with a test light or meter leads, just touch the pins to get a voltage reading. In this case it would be best to use a multimeter to start with, just to verify there is a full 12volts at both relay pins.
This code setting is due to no voltage present at the PCM pin 46 (Fused B+) pin. So, there might be a broken wire in between the PCM and ASD Relay location. I remember these vehicles having a lot of corroded connectors back in those years. If you need further wiring diagrams just let us know.

There are also a couple differences for "Early Model" and Late Model builds for that year. Some of the PCM connectors can have just 40 pins, 38 pins or 38 pin connectors with another connector going from pins 41-80, so if you see something different you can leave your VIN and we can look the vehicle up that way.

https://www.2carpros.com/articles/how-to-use-a-voltmeter

https://www.2carpros.com/articles/how-to-use-a-test-light-circuit-tester

https://www.2carpros.com/articles/how-to-check-an-electrical-relay-and-wiring-control-circuit

The PCM relay is reading 10volts on both pins? I'm going to look in OEM wiring diagrams because I don't even see a PCM relay in the aftermarket diagrams.

Okay, Fuse 14 30amp feeds the PCM and ASD Relay, so are you saying you have 10volts at that fuse but 12volts at the ASD Relay? There is a splice where power splits off to the PCM and then to the two ASD Relay feeds, the Splice looks to be internal to the Power Distribution Center where the ASD Relay and that fuse is located.

So here's the test we need you to do, with the key On, not cranking, just measure the voltage from the Fuse 14 30amp to either of the ASD Relay feeds with the relay out.

Can you also measure from Battery Positive to Fuse 14, I think you may find a 2volt roughly, but check that as well real quick.

And then Fuse 14 to any other Fuse in that box, such as Fuse 2 20amp, Fuse 4 40amp, Fuse 6 40amp, etc. I just want to see if there are any other voltage drops in that fuse center

We need to see if there is any voltage drop occurring between the Fuse 14 and the ASD Relay location. I think these wiring diagrams are not complete for internal circuits inside the Power Dist Center. I'm going through the OEM wiring diagrams right now. But I'm wondering if there is a cracked solder joint inside the Power Dist Center.

I'm not sure this diagram is correct, if you have 10 volts at that fuse and 12 at the ASD relay,
You can see all of these Splices are internal to the PDC, so a crack in any of those solder joints can cause an issue like this, especially with the Fuel Pump relay being on one of these splices, when a cracked solder joint gets hot due to current flow, the gap in the crack can widen causing intermittent issues like this.

I almost want to have you put 12-volts to fuse 14 (the fuse at 10volts) and see if the engine starts. That low voltage at a fuse like that can be internal to this design of the PDCenter. Id like to pull it apart and solder up any broken joints inside. Shouldn't be too hard to do. I would also check to see if there is low voltage on any other fuses. Because that with any voltage drop readings to B+ would give a clearer indication of what might be going on here.

If the voltage is reading only 10-volts there, you would only be bypassing the internal circuits of the Power Distribution Center, when you measured the voltage there did you have the Fuse 14 out? Is it one of those encased fuses? I'm just wondering if both pins where the fuse sits has only 10 volts. And do any other fuses in that box read the same?
Diagram 1 below shows the internals of the PDC, you can see it's a straight feed from the battery.

Double check your readings though, make sure that's really what you have on that fuse. I'm not sure how you are getting 12v on the ASD relay since its fed by Fuse 14. Did you have the relay out when checking the 10-volts?

And this must also drop the ASD voltage down as well, correct?
Try this test with the ignition on. That low voltage has to be causing the P0688 code; We just need to find out what is causing the drop off like that. Is it something inside the Power Dist Cent, or something after the fuse pulling the circuit down? The 2nd diagram shows it's a pretty straight shot from the Battery.
Fuse 14 has 2 legs on it, one coming from the battery and the other going to the relay, that's why I am asking if both legs of Fuse 14 drop to 10-volts.

This is some good info on the ASD Relay sense circuit for the PCM.

Okay, did you happen to notice any corrosion inside the PCM connectors while you were placing it? I'm going through TSB and Recall info. Here and there are some issues with the PCM connector seals being out of place. It doesn't apply to all vehicles, but this is a Recall. I'm going to post this for you. It's very strange that both legs of the fuse drop off like that, really only the leg of the fuse that's connected to battery power should even have voltage on it.
With the fuse out, the 2nd leg should be at 0volts. Thats what is confusing here.

Okay, does the PDC have connectors on the bottom of it you can inspect for corrosion?

This is the Recall notice on the PCM connector seals, although I would check other connectors and repair any corroded grounds.