From submitter azgli: The speaker system at a friend's party was missing a proprietary 13-wire cable between the main unit and the speaker controller. This was my solution to the problem - 13 individual wires insulated with Scotch tape! More Scotch tape kept them from shorting when the sub started rattling things around.
The transformer in submitter onecardshortof52's Logitech speakers was humming, but they couldn't be fixed without destroying the shell. So, after taking them apart, splicing some wires, replacing the power source, and giving them some stylish new resonance chambers (paper coffee cups), onecard now has a functioning set of desktop speakers.