Hyundai Elantra 2003 Won't Start

We have a 2003 Hyundai Elantra, 6 Cylinder Engine, with 65,349 miles. Yesterday, my husband was driving and his lights got really dim. He parked at a Jack in the Box, and his car died. He got a jump start then, and was able to get the car home. However, once home it died again. This morning, we tried again to start the car, and ended up getting a jump. The car started, but when he put it in drive, the car died. I think it is the alternator. My husband's father is an old school mechanic, so he disconnected the battery with the car running, and the car died. He also thought it was the alternator, however when he took the alternator to our local auto-zone, they checked the alternator and said it was fine. We then hooked up a new battery, but when it was disconnected, the car died again. I think Auto Zone was wrong, but just in case, what else could it be? Any help is greatly appreciated!