2001 Saturn l200
 

Car starts then dies, I try given it gas but it just quit. Just purchased a new battery for it but it is still doing the samething. What could it be?

what is the status of the security light on the instrument panel
1) when you get into the car
2) when you are trying to start it

This is the expected behavior if the security system thinks it has been tampered with.

Have you to make sure you're getting adequate fuel?
It could have a clogged fuel filter or other issues.
Does your exhaust smell like sulfur or rotten eggs?
It will have a clogged Catalytic converter if so.
Security light? refer to derf's post.
Have you checked for any trouble codes? You could have a sensor going bad that's causing the issue. i.e. coolant temp. sensor.