The Bose Acoustimass III system consists of two small cube speakers and one subwoofer unit called the Acoustimass bass module. If the subwoofer stops working, three points can be the cause of the failure. The Bose Acoustimass III is a passive system, meaning the speakers do not power themselves, but instead are connected to a receiver or amplifier. Thus, the amplifier, the speaker between the amplifier and the subwoofer, or the subwoofer itself could be the issue.
Disconnect the speaker cable from the back of the Bose Accoustimass bass module and connect it to a subwoofer that is known to be working. If the subwoofer works, the bass module needs to be replaced.
Disconnect the speaker cable from the back of the receiver or amplifier you are using and from the back of the subwoofer in Step 1.
Connect a speaker cable that is known to be working between the back of the receiver or amplifier and the back of the Accoustimass module. If the module starts working, then the cable was the issue.
Disconnect the speaker cable from Step 3 from the back of the amplifier or receiver, then connect the cable to the subwoofer port on the back of an amplifier or receiver that is known to be working. If the subwoofer works, the receiver was the issue. If the subwoofer still does not work, verify that the speaker cable is in the subwoofer port of the receiver/amplifier and that the cable is connected securely to the subwoofer.