I don't know much about cars but I do know something about electricity. I will go with the bad battery guess. The "12v" battery is actually made up of 6 2.1v cells. If one of those cells is bad a fully charged battery will provide 10.5 volts which is enough to get the engine going though slowly and will take a couple of tries. Once going you are good because the alternator is running the car and will place a "surface charge" on the battery that allows is to provide 13 or more volts. The surface charge fades fairly quickly but will persist for short stops and allow you to restart the car.
Take the car over to autozone or advance and they can do a free check of your battery for you.
If I'm being stupid someone will point it out soon enough.
