You have 3 possible errors
1. The cables is internally damaged. You would need to tester to see if you have continuity or a lenght of wire, battery and a small bulb will do.
2. The subwoofer is busted, I cant think of any way to test this but to bring it to one those Bose dealers and have them test the subwoofer, assuming they have a similar unit
3. Configuration on your AVR is incorrect