Drove to the store and everything was fine. Drove on the highway to another store and in the 10 minutes i was in the store the battery was dead. Waited a few minutes, car almost started. My gf came and jumped the car. Took about 10 minutes for it to charge enough to start. Drove home on the highway. Parked it in the garage. Starts right up again. Volts at battery and alt is 13.8 with the electric fan running. Went to shut the car off and the car didnt want to shut off. Had to turn the ignition off a couple times...car can be started without a key. Any ideas what to look at? Alt tested good at the store