2002 Ford Explorer Several problems that may be connected..

I have several problems that are taking place. When I turn the vehicle off, remove the keys, and get out off the car, the radio stays on. The interior lights go out like they are suppose to but the radio will play until it is timed out at 10 minutes. Second thing is that my electric locks are not working(none of them) with either the key fob or by manually pressing the lock buttons. If I disconnect the battery and reconnect after 20 seconds or so, the locks will work as they are suppose to for about 2 days and ten quit. This is driving me nuts so any suggestions will be greatly appreciated.