Why does my radio automatically turns on and run the battery down?

What is your question?

The battery is run down, I charge it, I drive the car 3 to 6 miles, shut it off, make sure the radio is off. Let car sit while I'm working, or overnight. Go to start the car again and battery is dead. Charge it and start the car, the radio is on the FM Public Broadcasting Radio Station. I pulled Radio fuse, now have no Instrument Panel Cluster gages. Replace Radio fuse, and now all gages are running backwards. But left overnight, car started.