Key snaped off in ignition got it out now car runs 4 10seconds gr

The key's to the Grand Am's have a security device of sorts in them. Thats what that little black thingy is on your key, if you ever wondered.
But, if this device isnt in contact with your ignition, it wont let you drive it for long. This was done to stop people from breaking the ignition switch and stealing them. you may have to get a new key from pontiac, but you can probably have a locksmith make you a new copy on the replacement key.

The New Key you are using is a duplicate?
The Original Key has a Security Chip in it.
Take the broken head of the original Key and tape it to the steering column right near the ignition cylinder. Now use the New Key and restart the vehicle. It should now stay running.
The lack of the Security Chip allows restarting, but then shuts the engine down after 10-seconds. 3-tries and after the third, it will not allow it to Start for approximately 30-minutes.
This Security Chip sends a signal to the ignition sensor allowing the vehicle to continuously run.

Let me know if this helped....