You might have a case of failed speaker amplifiers. Each of the speakers have a built in dedicated amplifier deep inside the speaker housings. They are a bear to replace but are rebuildable. I think the cost is about $100 per speaker and there are four. A quick search on the net will bring up several places that do the rebuilds.
I too have trouble with my system. I plan to upgrade the car to a Pioneer receiver and elimate the Bose components. I can get the receiver+speakers+wiring harness from Crutchfield for less than the cost to repair the Bose. And it is a much better sounding system when done. I plan to keep the Bose parts in case I ever sell the car and the next Owner wants it all original. I also plan to documet all of the work in digital pictures so the next owner has a frame by frame record of what I did and how to undo it.
Good luck on buying that 91! Sounds like a great car. Don't let the radio scare you off. We all have trouble and get 'Hosed by the Bose'.
Regards,
Radar
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1989 Medium Blue Metalic Convertible, Hypertech stg 2, 160 deg t'stat, 48,800 mi.
Save the Wave! "In God We Trust"