I have a 2002 Pontiac Grand Prix. For almost 2 years now, when I try to start the car it results in no sounds from the motor - this happens about 5% of the time. The other 95% it starts on the first try. The radio and lights turn on fine, but turning the key results in silence from the motor - at first. After about 5-15 minutes of continuously trying to start the car it finally starts with no problem. By continuously trying to start the car I mean turning the key from OFF to START and randomly it will start up normally. After I finally get it running, if I turn it back off and try again it starts fine. This happens in hot or cold weather. It is usually from a cold start, but I think it has also happened while the engine was still warm.
Let me know if you need any other information.