I have a similar problem. I have a 2002 Sonata 2.4l base. The car sat for awhile while I was waiting for parts for an unrelated problem. When I started the car my the alternator was frozen, would barely turn. I got a rebuilt alt online and installed. Now I have a alt light on constantly. Didn't have it before. With the battery charged it looked like the alt was only putting out about 12vdc and it dropped as the car ran. I took the alt out and had it checked at Autozone. They say it checked out fine. Alt was putting out 14 to 15 vdc. I put it back in, checked the grounds, fuses, belts and still not charging. Could the alt be good, but the Voltage regulator be bad? I'm not sure if the regulator is checked when they run it at Autozone. The alt is definitely not putting out anything. The output is whatever the battery is at and goes down as the motor runs. Does anyone know if there is a fuseable link or another fuse I might be missing? Do you think the regulator is bad and not telling the alt to put out? I'd go out and by a new alt if I knew that was the problem, but I don't want to spend $200 on a chance. Any help would be appreciated.