I had the serpentine belt break due to the AC compressor burning up. I have replaced the compressor and belt but the warning lights are staying on and I'm not sure if the alternator is charging. Could the overheated compressor have taken out the alternator also?

Typically AC compressors 'Sieze' up. When that happens, the belt can't spin the compressor pulley and it breaks. I really doubt that any serious heat came from the compressor before it siezed, and therefore I would really doubt that the A/C compressor 'hurt' the Alternator. You very well could have seen/smelled when the rubber belt broke. It would most likely keep spinning over the siezed pulley for maybe 30 seconds or so, in which time it would drastically heat up and smoke.

When the belt broke, a warning light came on the dash to warn that the car wasn't charging. I am not sure what other light(s) came on, or which light(s) are 'staying' on. Perhaps you could explain what happened after the belt broke. Who repaired the car? Were the warning lights on when you got the car back from being repaired? Please refer to the owners manual and list specifically which lights are staying on.

Thank you for the reply. The whole row of warning lights are on. This started when my wife came home after the belt had broken. I am doing the repairs, I have replaced the compressor and I am waiting on the right dryer to finish the AC fix. I don't know what would cause all the lights to go on simultaneously. I assumed it was the alternator not being turned by a belt until I replaced the belt and still have the problem.

Make sure a wire wasn't broken during the repair and belt flapping.