Confused.....01 cavalier

Alright so heres the deal my best friend has and 01 cavy. For about 3 or 4 months the battery light has remained on. Meaning lit up on the dash. Well she got in to drive the other night and notice all she was running on was the day time running lights. Then 1 by one the lights started coming up on the dash. First the abs the the traction like then the air bags. She managed to get it home and in her driveway and as soon as she put it in park the little light with the wrench came on and the car died. So the next day i changed the alternator for her and the car started right back up. But the battery light remains on. What is causeing the battery light to stay on. Any suggestions. Oh and the wires that goto the plug for the alternater doesnt seem to be hot??

Thanks

Do an easy check to see if the battery is charging. With the car Off, measure voltage across the battery. It should read about 12 volts. Now with the car running, it should read around 14 volts I think. Turn on the headlights, it still should read 14 volts or more. If it reads less, the battery is not charging or is just marginally being charged. Something is wrong with your charging system.

The battery light isn't for the battery, it indicates (almost always) a bad alternator. If you've replaced it then go get the codes cleared (Autozone, Advanced Auto, etc do it for free). If it comes back, check the ground on the battery, get the battery tested (those same places do it for free), and if that all fails then pull the alternator out and double check your wiring.