Well the PIP sensor triggers the TFI module and the TFI provides a signal to
the computer. Do you have a tachometer and if so does it show a valid
rpm when you crank the engine?

Does the engine run if you spray some starter fluid in the throttle body?

The computer should ground the fuel pump relay for about a second
when the ignition is turned on. It should ground the fuel pump
relay as long as the engine is cranking or running.