Another Issue with Hum.....Advice Needed

I know this has been beaten to death, but I recently introduced hum to my system, and am having a hard time figuring out how to resolve it.

I recently added to my sysyem an active subwoofer that is being fed a speaker level signal from my Receiver's front channel speaker outputs. When the receiver and subwoofer are both turned on, there is no hum. When I turn off all components except my subwoofer and 2 channel amp (I like to leave all amps on), a fairly loud hum can be heard from the subwoofer. The entire system was dead quiet before the sub was introduced to the system. This is not an issue when listening to music, but it is annoying and worrisome when the system is not in use (standby).

I should add that all components (Receiver, DVD player, CD Transport, DAC, etc. are all plugged into a VansEvers PLC and I have decent aftermarket power cords on most components, including the new sub. I suspect some sort of ground loop, but I have no idea how to resolve this. Any ideas would be apprciated.
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I wonder if you receiver switches inputs / outputs via relays, maybe when the receiver is off, and the system is on standby it might be leaking some signal to the subwoofers input (very low voltage -enough to affect the subwoofers input/amp but not and actual speaker...just a thought.
Hey, if you can bear to turn off your receiver (an amplifier itself), you can just as well turn off your subwoofer. Don't sweat it - the potential sonic gains to be made from leaving a SS amp always-on probably aren't detectable in a sub anyway (and that's not even considering that most recent subs use lower-fidelity 'Class-D'-type internal amps to begin with). Or, leave your receiver on. I'd just eliminate the symptom and not lose any sleep wondering about the cause...
Thanks a lot for the responses so far. One Audiophile, I think you are onto something. I know for sure that my Denon receiver uses relays for switching. This may be what is causing the hum.

I have another sub I only use for movies, and I think I'll hook it up to the receiver the same way as the other sub and see if the hum exists. If it does, I can assume that it is not the sub amplifier, and is most likely the receiver. Thanks again for your opinions.
I had a similar problem years ago and it ended up being the subs auto turn off was not functioning. What you could try, if you must leave your receiver on, turn off the speakers switch if you have one, mute the whole thing or put your receiver in standby. Try these and see after 5-10 min. if the sub turns off. If the sub still stays on, disconnect the sub speaker input and wait again. If the sub stays on, which it should not, then the auto on/off is shot. Sub amps are not meant to be on and idle all time. As a last resort, if you want to cut power to your sub without turning it off, if you can, plug it in the receivers switch recepticle and turn your receiver off or standby.
If it is a grond loop and your sub has a 3prong cord, try a cheater plug.