The oil level sensor has nothing to do with the car starting or running, $1100 is not a reasonable charge to replace it, either.
Ignore that until you get the car running.

If the problem is that the engine dies and the starter won't engage, I'd replace (or send to DJ for repair) the Relay Control Module. To confirm it's the RCM, the next time the starter wont engage, turn key to Start, let key relax back to "on". Wait 45 seconds. Does engine cooling fan start running at very high speed? If so, it's almost 100% certainly the RCM.