97 Regal GS Starts then Stalls

I have been chasing a problem around my Regal for a few days now. Went through all the engine codes and replaced all bad sensors. I can start the car, but it dies shortly after. You can hear the fuel pump running with the car, as soon as it stops the car dies. I changed the fuel filter to find the car runs for a little while longer before the pump kicks off. I found the relays warmer than I felt they probably should be, so I changed them both (f/pmp, and f/pmp spd cntrl relays).
If I start the car and give it a quick snap of the throttle the pmp will stay on and it will idle, but as soon as you touch the throttle the pump turns off and the car dies. Any help is greatly appreciated.

My 99 just had this problem - it turned out that the fuel pump is run at full voltage for a few seconds just after starting, and then a relay places a resistor in series with the fuel pump to run it at a slower speed.

Apparently it is quite common on the GS for the resistor to fail open. When this happens the fuel pump will stop shortly after the car starts, and the engine will die. Of course, you can immediately restart it and it will run again for a few seconds.

The resistor is located on the body channel under the passenger side front fender.

Unfortunately, because of the timing of the failure and the time of year this little gem of knowledge cost me about $300 in towing and dealer repair costs!

Hope this helps.

Bruce