2006 Hyundai won't start


I just bought a 2006 Hyundai with 2,800 miles. For 32 days the car started and ran well then on the 32nd motning and again on the 34th morning it refused to start. The engine turned over but the starter did not engage. Then on both occasions,later in the afternoon, it did start. I took the car into the dealer since it is still under warranty. Now after they have had the car for 5 days, they are telling me, they can not find anything wrong with it and they want me to come pick it up. Logic tells me that if it didn’t start twice then at some point it will not start again and there must be something wrong.

What could possibly be wrong and what should I do about it?