1997 Pontiac Grand Am GT starts and shuts back off.

Have you changed your key or anything to set the cars security system off. I work at a small car lot and have run into this a few times. Look in your owners book and see if they give you a reset procedure. All GM cars a a bit different but most leave the key on till security light stops flashing and then try to restart.
Doesn't allways work on the first try. Hope this helps.