I hope Current Audio put you through several paces to try to eliminate this problem before they spent their money on an exchange! Most of what is suggested here should have been suggested by them.
But wait, there's more! The cable is connected to the cable box. The cable box is connected to power. The cable box is connected to the Denon.
When you disconnect the HDMI cable, you disconnect the cable box from the Denon. You disconnect the cable ground from the Denon. You disconnect any hum that might be caused by the power connection, too. In short, disconnecting the HDMI cable disconnects several things.
That's the second place you should have looked. The first place would be the cable connection itself, by disconnecting the cable from the cable box.
The third thing to do is to introduce an audio isolating transformer between the Denon and the subwoofer. Put it at the sub end of the cable. If that doesn't work, put it at the Denon end of the cable.
Basically, keep trying different best washing machine in india best washing machine in india
things. The only thing you should NEVER do is to take the third pin off of a power plug. That can be an actual killer move.
One system had a hum that I could not get rid of. I lucked out in that there was a copper water pipe on the other side of the wall from this system. I connected the receiver to that and the hum went away. (But I had to check several places to attach the ground wire to the receiver -- some places made more hum!)
When you solve this, you will see some subtle difference between the ways the systems are hooked up. You might even have an accidental short to ground in your problem house. (To verify, disconnect all wires from all components and measure resistance from the wires to electrical ground.)