Head Unit stops powering on

My friend drives a 96 Saturn SL2.  Her dad put in a new head unit, which worked fine at first.  However, it quickly stopped powering on, and started to power on randomly and then off again.  I immediately assumed it was a loose wire or a short somewhere.  I finally got a chance to look at it today, and rewired the whole thing.  It didn't come on.  I checked all the fuses and grounds, and everything there is good.  Later, however, we heard it beep after we turned off the car.  So we turned on the car, and voila, it turned on!  It ran great for a bit and then was off again.  Then later it was on (all of this without the car moving at all).  Finally, we noticed that the seat belt light DOES NOT come on when the radio doesn't come on.  When the HU does power on, the seat belt light comes on and dings.  Does anyone have any ideas at all on this one?  Is there any spot in the car where the seat belt light wire splits and goes to the stereo or anything like that?  Or does anyone have ANY ideas at all on this one?  I only get to see her a couple of times every 3 months, so I would really like to get this fixed for her.

Any help is appreciated.

Kevin

Found out that in a saturn, the Rear defogger, radio, chime, all run off of the 'chime module'.  We're going to replace it and I'm sure it will fix our problems.

Thanks,

Kevin