97 2.4L Sunfire starting problems

Every so often it will not start. It attempts to turn over and after a few try's and just letting it sit for a few minutes it will eventually start and runs fine after that, until I turn it off and hope that it starts back up again. This problem started to occur shortly after getting the battery replaced. The battery keeps its charge and the alternator works fine. The dealer thought it was a problem with the factory installed alarm system and removed it and rewired it to factory specs, but a week later the car wouldn't start again. It happens very sporadically, sometimes once a week, some times every other day.
Anyone ever experience this problem?
Thanks