You need to clarify the part about the radio not turning off. Do you mean that you can’t physically turn it off with the ON/OFF control on the radio or that it won’t turn off when opening the door?
If it’s the fomer there could be a problem with the ON/OFF control in the radio head; especially if that control uses a push button function to flip between ON and OFF. That would not be a rare problem and if so you would need another radio head unless you have the DIY ability to take the head apart and replace the switch.