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It sounds like your dizzy cap isn't lined right which causes the engine to stay running after the ignition has been switched off. i had the same problem with my fiesta
Timing issue - either cam or ignition.
Not running on all cylinders? Bad spark plug or wire? Bad ignition coil (if C.O.P.)? Bad valve? etc.?
What_is_a_loud_humming_from_car_light_motor_after_in_lowers_down_and_closes_on_your_1997_firebird
It could be the electrical ignition system. there is a recall, dealers will replace the ignition relay free of charge. check it out. Pontiac tele. #1-800-620-7668
I believe this usually this happens if the fuel / air mixture is not rich enough (too much air / too little fuel) which causes the cylinder heads to get too hot which means that any unburnt fuel in the cylinders will continue to ignite even after the ignition has been cut.
Head lights on?
How easy is it to replace head gasket on 1994 firebird lt1 motor
look at the fly wheel to see if it has any missing teeth that might be the problem
You are more than likely hearing the electric fuel pump running. If it is noisy then it will fail in short order.
Pre-ignition.
Generally the most common problems with these engines is fuel-related, though ignition can be a problem if the blade has struck something shearing the key.