I think your crossover may be set to high as well as the volume. Set the volume at about 1/4 and the crossover at about 80 to start with. If you set the crossover too high you will get a humming sound.
Ben, it's probably not the cable, although I did use that same video cable (which is thicker than their audio cable) and changed it to the audio cable because the metal wrap just before the rca jack was causing a hum when it was fussed with in any way. This was also probably just a bad cable and not a video vs an audio cable issue at all, but thought I'd let you know. I also had the audio cable handy at the time.
The actual problem you are having is probably one with the DLS itself- many of the current batches that just went out are having trouble with the auto off/on switch and I have heard of your problem before, too. I've done a lot of fooling with my crossover settings and have had no hum issue. The volume should really be set up to match the volume of your other speakers (calibrated using a disk if possible)- 1/4 up is all I think you will need on the "Tiny Mighty" in that space.
I agree with jason, though and would make those adjustment he mentioned first. That's pretty much how I have my DLS set up.
Also be sure to check for the auto on/off problem as PE will ship you out a new amp at no extra charge if your DLS is part of this bad batch and you don't even have to send the sub back. Good luck!