So the engine cuts off while driving? And then you say it will turn on but not turn over-does that mean with key on warning lights and dash gauges come on, but the starter motor will not come on and spin the engine to start? Or does the engine crank over but won't start?
An engine shutting off while driving could be many things electrical, could be the computer, or it could be an ignition part that is getting warmed up and failing. Any previous symptoms with the car, hard starting, or not starting?
More questions than help, I know. The right time to check if ignition is working or not, if the spark plugs are getting voltage to spark, is when the engine shuts down and won't start right back up-that is when to check for spark and if no spark, then it is an ignition problem. Could be the ignition module, the computer, or possibly the crankshaft position sensor- computer uses that sensor information to cause the ignition to create spark.

If you find you do have spark with the engine cranking over, there may be a problem in the fuel pump circuit. Better have a shop run some diagnostics.
Be sure and check for any trouble codes-have the computer scanned. If codes are present, they may point to the solution.