What is wrong if the radio in your 2001 Chevy Impala won't turn off but the dome light does?
The 2000 and up Impala's have a feature called RAP or Retained Accessory Power. This allows you to operate your radio and windows without the key or car being on for 10 min after you shut off the engine opening the doors will shut off the RAP and you will need to turn on the car again to roll up windows and such. I don't know what the cause of it is but we had that happen one day about 3 months ago. Prior to it not shutting off we got "garbled" reception from the radio..then when we parked the vehicle and started to exit the radio didn't shut off. We found the fuse (in the fuse box on the passenger side) and pulled the fuse and put it back in. We havn't had a problem since. Doesn't help you with the "why" questions but may help others from a dead battery. Karen