Car will not start when parked on an incline?

My car runs great but sometimes when I park the car at a slight incline, the car will not start. When it does have the problem, if I leave the car for one day and come back, it starts right up. When it is having the problem, the key will turn over, lights will be on, and the car will not even try to start.

Additionally, when it is acting up, I can start the car with jumper cables.

Oddly enough, this problem has never happened on a flat surface, only occasionally when the car is parked at a slight upward angle.

I have replaced the slave cylinder and neutral safety switch with no luck. I have also brought the car into a mechanic, but they could not diagnose the problem because they could not duplicate it.

I appreciate any help as this has been puzzling me for almost a year now and was wondering if anyone has ran across this problem before or knows the solution.

Thanks, Tim