Key turns over, no clicking but car won't start.

I just bought my 1992 Geo Prizm yesterday, and was in the process of driving it back from the northern part of VA, back to the Hampton Roads area. Stopped for a pick restroom break, and when I came back out to my car it wouldn't start. The key rolls over, all the dash lights come on, headlights worked, but the car just wouldn't start. Though it didn't make any clicking noises. After calling for AA to come and pick it up, I waited for about 45 mins with the hood of my car up and tried starting it again. It started without a problem. The car wasn't over heated, and the battery still had plenty of juice so I don't think this is a battery problem. The woman I bought it from just had the water pump replaced because the pervious one had gone bad.

Any suggestions?