It can be hard to diagnose something like this over the internet. All I can really do is help educate you and hopefully you can figure it out.
Normally when there is something blocking the communication between the ICM and the PCM, I would expect to see some trouble codes in the computer (2xx codes pertain to signals the computer receives from the ICM).
I don't know what diagnostic tests your people performed, so I can't really comment on what they did. Obviously the problem isn't in the ICM itself, (or in any of the other parts you've replaced).
If you get a wiring diagram, you might be able to rewire the thing to see if that fixes it. I expect it would be easier to get a wiring diagram and check the continuity of the wires with an ohmmeter. I don't have a manual right in front of me (but the local library does, so that's where I go when I need the manual).
The computer will run the fuel pump for a few seconds right when the key is turned on, then wait for the PIP/TACH signal to indicate that the engine is rotating. When that signal isn't received, the pump stays off. Your experience with the fuel spray from the fuel rail would be consistent with this scenario. But I'm afraid it does little to help diagnose the issue. What happens if you ground the fuel pump test lead in the self-test connector? Does the fuel pump run all the time? Will the engine start?
I'm afraid I don't have much good advice here. I'm not sure what conditions would cause the ICM and PCM not to communicate but not leave clues in the computer. At this point, the best thing to do might be to talk to your technician tomorrow and see if you can get more information or get him to look at it in more detail. He might be able to shed more light on this than anyone.
Let me think on this some more, too.