Check the engine grounds again, mostly the EFI harness grounds that attach to the back of the cylinder head. The ICM could have died just being on the shelf, it happens.
One thing that is interesting is that re-connecting either the cam or crank sensor with the key-on causes the fuel pump to run. This means that the ICM sent a reference pulse to the ECM. That is, the ICM thought that the crank and cam signals were properly seen. And sent a reference pulse.
I can see this possibly occurring with the cam sensor connector, but shouldn't with just the crank signal being toggled. However, I've never tested this, may be a good thing for me to try someday just to see what happens.
Operating properly the ICM needs both crank and cam signals before it will send a reference pulse to the ECM. The ECM in turn will start to fire the injectors (batch fire during cranking), and turn on the fuel pump. Which is what you are seeing. The ECM will continue to run the fuel pump as long as reference pulses are received. They stop, 2 seconds later the ECM cuts the fuel pump.
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