2002 Lexus ES 300
 

Left my car running while detailing it today, no issues. When leaving, my battery light started to flash and then the car stalled. I couldn't start it back up. Had to have it jumped. Went to AutoZone, had battery replaced (it was over 3-years old). Car started right up. One hour later, went home, parked the car, and then attempted to start it again. The car wouldn't turn over. It sounded like it wanted to, but wouldn't. So, is this an alternator issue? Or starter? Thanks...