1993 Honda Del Sol Car turns over but wont start.

Engine Mechanical problem
1993 Honda Del Sol 4 cyl Two Wheel Drive Automatic 120000 miles

Occasional I have an issue with starting the car. First I try to start it and it turns over and seems to start but then dies right away or shortly after. Then I try to turn if over again and it turns over but does not start. If I turn it off and leave it for 10-15 minutes it will start up and run perfectly. This happens randomly and Its been hot/cold/raining/dry and it doesn't seem to matter. I did have someone try to steal my car and they messed up the ignition switch but I got it to go back to the off position and it worked fine every since then till just recently. It seems to be an issue were something shuts off the fuel after it stalls and it resets shortly after. Any ideas of where to start would be good.