Sources suggest that the 2002 Chevy Cavalier does not have a fuel pump kill/shut off switch.
If the fuel pump isn't running either the fuel pump has failed or the vehicle is in "theft mode". If you crank the vehicle and it starts, runs for a short while, and then dies, it's in theft mode.
To get it out of theft mode follow these steps:
Turn the engine off for at least 30 seconds.
Turn the key to the run/on position and let all the bulbs do their self-test.
Start the vehicle.
Let it stall.
Leave the key in the on/run position for 12 minutes.
Turn the engine off for about 20 seconds.
Try to start the vehicle normally.
If it starts and runs without a problem you will need to replace the lock cylinder and theft sensor.
Taking good care of your vehicle can make the difference between being the proud owner of a good looking, long lasting, reliable machine, and saying goodbye to a rusty, faded-paint jalopy that fell apart or broke down long before it was designed to. Check out some car care tips at Kbb.com.