Chances are since your car is 6 years old, very little mileage, it wasn't driven too often or for very long distances. Your battery was draining slowly and not receiving a full charge due to the alternator having such a short time to do its job. An alternator works harder to charge a battery that has less voltage present. You would think something that has been used for so little time would be less worn out, and still have a good amount of life left. Not in this case....

Make sure the mechanics give your battery a full charge before they install the alternator so that it wont be working double time to charge up your battery while powering the rest of the vehicle electrical system.