Have you tried plugging in a stock computer to see what happens?
I have a few other thoughts and/or questions. Full disclosure: I know very little about the PxS, so these may be way off base.
Does the type of ICM matter with the PxS? If so, are you sure you have the correct one? I don't remember all of the differences in the two types, but I know that how the spout signal is used is one of them.
Does the PxS allow you to tell it how many cylinders you have? If so, is it possibly set up for the wrong number of cylinders? Sometimes there are rpm windows where no spark is provided for safety reasons. If the cylinder settings are wrong it might prevent spark at cranking rpm. Not sure what the spout would have to do with that, but could be related to my first question. I've seen MSD boxes cause similar situations, but you said you tried bypassing it and it didn't change anything.
Does the tach read in either scenario?
Have you tried setting the advance in the PxS to zero? I don't think I can articulate my reasoning for asking this, but I'm thinking something along the lines of it being possible that if the advance is set to high the PxS could be getting the signals to open and close the coil circuit confused.