Sounds like the alternator to me. The battery is probably dead, but the charger is reading false. I've had that happen before. Take the battery out of the car and put the charger on it over night. See what happens then. To test if the battery is dead, turn on all the lights and hold the horn down. If the horn fades to quietness, the battery is dead, if the horn keeps going, there is obviously charged. If the battery has no charge, blame the alternator