I have a 1996 Maxima. The entire Bose radio/tape unit will not turn on.
The strange thing is that I could get it to work by cutting the power to the unit (removing the fuses AUDIO and ELEC PARTS for a few seconds and plugging them back in).
However, it would stop working the next day or even after a few minutes or few hours with the car off.

 

You could try adding a ground wire from the radio case to a good chassis ground. But I kinda think that your head unit is taking a jump and needs to be replaced.

 

Check ebay for a nice used unit.,