Driving my 02 Grand Prix 2.4, starts ok but a minute later dies while I'm driving. I change shift from D to N and start engine again and I can be able to drive, minutes later, car dies again, repeating the procedure again and starts one more time. Any ideas?

This car has been a nightmare since I bought it used 06/26/14. Filled up tank, went home, parked for 4 hours, went to store but couldn't drive it home because it ran maybe 2 minutes then engine shut down. I attempted to start it several times to no avail. The gas gauge says full but low fuel light on.