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It's been a couple of years since I looked at them; but, if I remember correct, it seems there could be an easy check.
Since the Bose speakers have the power amps built into them, I think all you have to do is supply a 1 volt peak-to-peak, low power, audio signal at the high impedance input terminals with 12 volts supplied to the power supply terminals and you should hear the amplified audio.
Just worked on some recently. If I remember the orange wire was the +12 volts, black ground and the two other are the audio input. Forget what colors. As said you can inject any kind of low level audio in. You can kinda cheat and get an idea of if its working at all by rubbing your fingers on the other two wires and listening for some static or hum in the speaker. If your near any kind of florescent lights, you might be able to pick up the hum from them. Its just a quick check to see if its alive at all, but no check of quality.
Wondering what your original problem is, one speaker assembly or no sound at all.
From what I remember the few times I actually listened to it, I got some squeeling from some speaker, but I think sound would come out of all of them, once I got it passed the volume of the sqeel. It took some of them a while to warm up before sounding right.
Check out my post for your problem. It should be what your looking for. The second two might be easier to understand. The first one has more detail. Just stick with what you need to change to fix the problem, you don't need to understand the theory. Good luck