Did you charge the battery up after putting on the new alternator? It is possible to ruin a new alternator by overworking it if your battery is low on charge. Alternators aren't rwlly designed to charge a dead battery. They are designed to power a cars electrical system. And replace a small amount of power used up while starting the car or when the car is not running. Also I would have the battery tested. It may have a bad cell.
