the pip will come from the EDIS module. the EDIS will get the signal from the CPS and have the output for the coil packs... it will send the pip to the ECU and the ECU will work out the correct advance and send the SAW back to edis, which will adjust the timing of rth spark.
it;s dont like this because the EECIV unit isnt fast enought to calculate the spark real-time... they needed a second module with enough processing power to sort out the dizzyless ignition (thats wheer the EDIS comes in)
if the EDIS module receives no SAW then it will default into its own little limp home mode and fire the coilpack with a static advance of 10degrees. this could be your problem. it's got a spark so it'll fire up, but its running suck wank advance that its not enough to keep it running.
also get yourself a fuel pressure gauge on the fuel line... it could be that the pump is shit, and itll fire up on the pressure in the rail but the pump cant get enough in to keep the car running. oh and take the petrol cap off as the breather can get blocked and itll have issues (altho not as severe as what youre describing) get yourself a look at Autodata (im assuming the garage has a copy?) and check all the wiring diagrams in there... make sure youre getting the correct signals from all the management sensors...
oh and gine, fuel + spark + crank does NOT = fire up... the spark could be in the wrong phase