1993 Ford Probe poor engine performance

Starts immediately but runs rough and very low idle. Quits when the accelerator pedal is depressed. If you push down on the accelerator and then start the engine the engine accelerates fine but always quits within 10-15 seconds.

Here is what I have replaced: Fuel pump and filter. Distributor, MAP sensor, fuel pressure regulator. I have also bypassed the inertia switch and taken the dust cover off the fuel pump relay and manually held the contacts closed. None of these things made a difference. I have also looked for cracks in the induction system and it is air tight. It did run perfect for about 45 seconds once.

They took it to a mechanic and he could not figure it out. They cannot afford (as they are quite poor) to fix this car and I am trying to help them out. I am not a mechanic but have great troubleshooting skills, understand how engines work and have full knowledge of electrical systems but none of this does much good unless you have experience.