well it should run with fuel down the throttle, although it makes sense that the cause would be related to where it was last worked on, IE the fuel system
tyr another FP relay its under the hood either next to brake booster, or its over on pass side fender inside a little black box case thingy, a fuse over there that commonly is burnt, for the FP circuit
does the FP run when key is put in run position, or a few seconds?
if not then no power or ground to the FP
or not ehnough voltage to it, damaged wire gray one along frame rail
[jump orange wire to the gray one, at the oil switch on engine rear, or at the FP relay plug
pump will run constantly and full speed full pressure good and will fire up and run if wiring and pump are good
in the tbi engines distributor bushing wear causing erratic or loss of distrib pickup signal is common
also failure of the ICM in these is common as well
try a known good ICM first they are all the same on all the GM TBi engines 4 cyl to v-8 late 80s to mid 90s TBI any size engine 2.5 2.8 3.1 3.8 5.0 5.7 and 454 etc, car truck van etc, as long as TBI engine
and use heat sink compound, not dieelctric grease, under it
you want the solid white paste stuff used for computer processors etc or it will overheat and die on you and not start/run
if good ICM doesnt fix it then try a dknown good entire distrib