As I’m driving the car it cuts off, it doesn’t make a sound, it doesn’t hesitate cutting off and then it won’t start for about like 30 minutes. I just put a new starter on it.
Sounds like something is getting hot and shutting down and once it has a chance to cool it works again. This is common to electronic components. Most common failure component that acts like this would be the ignition control module. I have looked up the part and double checked to make sure it will fit your Saturn L200.