Chevrolet - Malibu :: 2003 - Hard Start Then Won't Idle

My car will start but die. it either wont turn over or if it does, the engine goes right off. The radio and lights work though. the throttle & iacv were all good. i got it towed and the mechanic brought it in his garage at end of the day. He said it wouldn't start so they left it for monday. The thing is that my ignition sometimes gets stuck and leaves radio & interior lights on. So when they tried starting car on monday, it was dead. They put different battery on & it started right up. they said everything else was ok. they charged my battery & I had no problems. until today, 3 months later, same problem. both times it happen when I am leaving work & both times it was raining & cold. Could my battery be bad? also wonder if place really checked everything out likethey said.