I dont know if our car problem is exactly the same but mine had a similar problem.
I have a 97 Grand Prix supercharged that was doing this very thing. When I start it up, it might idle 3-8 seconds, and less time than that if I pressed the gas pedal. I first thought the fuel pump was bad and replaced it, turned out it was not that (ouch $330.00). Turned out to be a speed control resistor used for the fuel pump. My 97 has 2 relays that run the fuel pump, relay 1 is called the fuel pump relay, it pumps up the fuel line and runs for a burst of about 3 seconds when I turn on the key. The other relay is called F Pump Spd Cont, and it works in conjunction with a resistor that mounts behind the right front headlamp down low on the fender well. The delco part number for this resistor on the 97 is 88951182. The electrical current flow is limied to the fuel pump through this reisitor and it allows it to operate at a lower speed. However if the resistor burns out, the fuel pump will not run long after the first relay shuts off. This relay is only available through your GM dealer or other delco sources, and costs about $58.00 (big rip off). I suggest you check to see if your 2000 is equipted with this resistor, I know the supercharged models use it. If your car has this F Pump Spd Cont relay you will find it in the fuse box under the hood by the washer resevoir. It is relay number 15. You can bypass the resistor by removing the relay and placing a jumper (I used a paper clip) across pins 3 & 4 of the socket the relay came out of. If this makes the car run, then you need a new resistor, or the wiring got damaged.