further diagnosis...

I started the car, drive 15 mins to the gym, shut off went inside for about and hour. Came out she started no problem. Drove 15 mins to the grocery store, ran in for 15 mins came out and she would NOT start. Tried 3 times, not luck...she just cycled but would not turn over. Batterty didn't die this time. I waited about 10 mins tried again this time she started.

Could this be related to the key or security system? If the key is faulty, would I still be able to turn it?