radio does not turn off when you take key out of ingnition and open the door dome lights do not come on like they should

Hello, This sounds like a bad door switch. Each door has a switch or sensor which detects when the door is opened. If the switch has failed, your symptoms would be replicated. In fact, the radio would shut off after 15-30 minutes, depending on the program set by the manufacturer. The other possibility is that the wiring harness for the door has decayed and cracked over time. This happens as a result of opening and closing the door for years, since the wires have to bend twice every time the door is opened and closed. I would inspect the harness first to ensure power is getting to the door switch, then test the door switch for operation.