Car randomly does not start

A week ago I replaced my car battery because it was not starting without a jump. It was fine all week then all of the sudden one night it would not start even with a jump. When trying to start the car it would make a slow spinning/whirring noise. It was towed to Triple A and they claimed that it started right up when they moved it into the garage. They think it is a bad alternator, but I a'm just not too sure.