Intermittent trouble starting just after installing new fuel pump

first need to make sure you have enough fuel pressure. Hook up a tester and check against the specs. if its too low, then your probably looking at a fuel pump. By replacing the filter, you allowed more fuel to flow. Also, make sure you are getting spark and injector pulse.

if it ran ok before you changed the fuel filter you may have lost prime and may have to bleed the injectors

It is probably one of three things. It isn't getting a proper spark, proper fuel, or proper compression. Good luck!--------------------------------------------------------------------------
VAS 5054A

Your alternator might be bad also, or the crank sensor

There's a computer controlled circuit that will kill fuel pressure on some cars right at the last inlet valve at the fuel rail.A bad key or ignition can cause this. don-ohio

Did you replace the fuel filter as well?

When your replaced the pump did you replace the fuel filter? You may have a fuel pump relay causing you some grief. I believe it is located in the engine compartment in the fuse center on the left inner fender. Check the relay and any related fuses. Check the electrical connection at the pump. They had problems with some of them and they would get kind of hot and distort and corrode. They have new updated ones that can be easily installed.

Check ground wires, add a couple extra, can't hurt is cheap and in most cases fixes the type of issues you described

did you reset the alarm/immobiliser system every time the power was disconnected???

the pcm may have a cracked board, i had an 88 cavalier z24 with the same problem, replced the ecu and it ran fine, the problem is that the boards inside the pcm crack and lose connection, the next time it acts up open the glove box and try tapping on the pcm, if the car responds at all, the pcm is bad