If the Bose stereo unit powers up but you have no or distorted audio, no FM, some/all speakers work intermittently, or the system is dead, check, the CDM (Tuner Pre-amplifier Box.)
It can be found under the dash board on the passenger side ('90-93 in most cases) or in a rear pocket on the passenger side of the vehicle ('94 and up).
I have seen the units behind the seat submerged in water and have corrosion, also check connectors below the CDM box.
When the head unit is turned on and off you should hear a click from the relay inside the CDM box. If you have snapping and popping from some of the speakers you will have to trouble shoot to the defective amplifiers separately.
Is it a defective CDM box or Bose amplifier? You will need to swap working speakers enclosures with nonworking speakers enclosures to determine if it is the CDM box or Bose amplifiers that are defective
http://www.carstereohelp.com/corvette.htm