Saturn died while driving and now won't turn over

The starter still works to crank the engine over? If so, maybe the fuel pump quit. Turn key to on, not start, you should hear the fuel pump in the tank turn on for a couple of seconds. If you hear it turn on, then gas is getting up to the engine, at least. If you do not hear the pump, try banging on the bottom of the gas tank-sometimes this will cause a failing pump to turn on one last time or two. If hitting the tank starts the pump working, the pump will have to be replaced. If still no pump, the pump circuit will have to be checked-either the pump is bad, or the pump circuit has a problem.
If you can hear the pump with key on, maybe the ignition quit-so then you need to check for spark on a plug wire. Sudden no starts like yours are usually gas or ignition related. If no spark when cranking the engine over, the ignition circuit will need diagnosing. If it does have spark, and fuel pump works, could be the injector circuit.
If you have spark and gas, check for trouble codes. Probably none, but you need to check. If any are related to the stall while driving, you are onto the problem.
Post back with what you find. Here's a quick test to see if gas or spark is the problem- as long as the engine cranks over, that is: spray some starting fluid into the air intake (take the big rubber boot off and spray inside the throttle assembly). Then try to start the car. If it fires up and runs a few seconds, you know it is a gas problem-the pump or injector circuit has a problem. If starting fluid doesn't cause a peep from the engine-doesn't even try to fire and run, it is probably ignition problem-check for spark.
Stalling while driving is an electrical problem, computer related. Common problems are the fuel pump (gas), the crank position sensor, ignition control module-both related to spark and spark timing, part of the ignition system.

Check to see if the cam shaft is turning while cranking the engine (broken timing belt) run fault codes to find faulty sensors.