CD/Radio works intermittently

I have a '95 Park Avenue Ultra, and my problem is that the CD/radio unit will just shut off completely every so often (power completely cuts off to the unit). Sometimes it goes a week without shutting off, and sometimes it will shut off several times in a 1-hour period. I had another radio unit on hand, and I tried that one, and the same thing happens, so I know it is not the CD/radio.
When it shuts off at times when the lights are on, the climate control temperature display switches to the daytime (bright) setting. I suppose this is because the message to dim the climate control goes through the audio system, just like the steering wheel temperature control goes through the radio unit (this stops working as well).
Another important note is that the interior light switch stops working at the same time the audio system shuts off. It usually lags by a few seconds, though. And sometimes the audio system has lost power, but the interior lights still work, but usually only for a few seconds before the lights shut off too. If I turn each light on individually, they all work. Also, all exterior lights are uneffected.
If somebody knows what the problem is, please let me know. Thank you!