Radio stays on when I open the door on 1995 Lincoln Town Car

First of all my digital dash clock went out...then when I have the radio on, shut the car off and then open the door (the radio is suppose to go out) but it stays on. I can turn the key back on then off and then it goes off. But if I let it set for more than a day the battery is dead.

Asked by for the 1995 Lincoln Town Car