Does the subwoofer stll hum when the cable bringing the audio signal to the subwwofer is removed from the subwoofer?

What if the subwoofer input is shorted?

I have a similar (36") Sony. It's power supply is a switching type power suply (not a linear one) and these type of supplies may be putting high frequency junk on the AC line (and radiating it into the ether as well). Perhaps you sub is sensitive to this junk.

This is unrelated to your problem, but light dimmer switches also put junk on the AC line and can cause a hum (or buzz) to come out of the speakers because one or more pieces of audio equipment is sensitive to it.

Paul

Here is a link to information from the manufacturer of most of my speakers, including subs, which addresses the exact issue with hum. Maybe it will be of some help.