I'm not very mechanical, but this sounds like a problem I just had with my Superformance Cobra.
I bought my car five years ago and it still had the same battery; I don't know how old it really was.
I was over at a friend's house the other day, and the car would no longer start. It seemed to us like there wasn't enough cranking amps to engage the starter solenoid. We brought the battery in for testing and, while it had registered plenty of volts, it only had 30% of the amps left. I bought a new battery and the car now fires right up.
Your old battery might be on its last legs.