Okay, I have described my situation above pretty well with the jumper wire in and the radio not hooked up to the TV. I just shot a little video, at the below link, that shows you the symptoms I have with everything plugged in. Take a look. The radio and television seem to have separate on-off knobs. There is no selector switch on the set anywhere to switch between one set and the other, Just their separate on/off knobs.
http://youtu.be/5jijSMlFs4Y