If the car just shut off on its own that isn't the starter. Sounds to me like your electrical connections, specifically your positive cable and connections. Don't just assume that the cable itself is good, I've seen more than one cable that was bad inside. So, start at the basics, check all the connections first, make sure they are all clean. Test the cables with a continuity tester if possible. You can also use jumper cables to make the same connections to test out the connections.
More than likely it is something pretty simple.
