If I am understanding correctly, the subs are picking up this hum without any inputs connected to them. In other words, they are connected to power only? Is that correct? It sounds like your plasma TV is generating interference that is being fed through the AC power cord into the power system and then through the power cord into the subwoofer.
The fact that plugging the plasma into a different circuit eliminates the noise backs this up.
It may be that your plasma is producing more noise than it should, and/or it may be that your subwoofer is more susceptible to noise than it should be.
Does the plasma being on and displaying all white generate noise in any other components?
You say that you get a very slight hum in the subwoofer. Does it change when plugging it into a different power circuit and/or when you remove the input cables? It may be that the subwoofer always produces a little noise, or if it happens only when the input cables are connected, it could be a ground loop. But this does not sound like your main problem.
The fact that sound hits a null every 8 seconds or so leads me to believe that the problem is tied to the plasma's sync rate, which will be different than the 60 Hz power frequency. Video and computer resolutions are typically based on a "60 Hz" timing that is actually "59.94 Hz". As this goes in and out of phase with the power frequency it will get louder and quieter.
Try feeding the plasma a signal with a different refresh rate. Use a computer as a source (ideally a laptop running on a battery to eliminate any concerns with ground loops). Try changing to different resolutions with different scan rates to see if the interference changes. If it does, that is a pretty good indicator that the circuitry in the plasma is generating the interference. The fact that it happens most when the plasma is displaying a bright white screen certainly points in this direction. That's when all the pixels are lit up, the plasma is working the hardest and there would be the most potential for noise generation.
It sounds like you have already done this, but if not, try unplugging all input cables from the plasma end of the cable (as opposed to the signal end). If this helps, they were likely acting as antennas and radiating the interference. Try connecting each cable one at a time, first with only the plasma end connected, then with the other end connected to whatever it normally connects to.
You may find that the solution lies in one or all of the following:
Make sure that the plasma chassis is properly grounded with a 3 wire power cord that connects to a good ground.
Make sure that the equipment that the plasma connects to is well grounded with a 3 wire power cord that connects to the same ground as the plasma.
Make sure that the subwoofer well grounded with a 3 wire power cord that connects to the same ground as the plasma.
If any or all of these components don't have three wire power cords, try adding a ground wire that connects to an existing screw on each chassis to properly ground them.
If the cables were making it worse, make sure that you are using high quality signal cables for anything connecting to the plasma.
If the cables make the problem worse and quality cables doesn't help, you want to try modifying the signal cables to disconnect (lift) the ground (shield) on the plasma end of the cables. This may seem counter intuitive, but because they are already grounded at the signal end, grounding at both ends in not necessary and it can cause problems.
You could experiment with reversing the hot and neutral connectors on the plasma power cord to see if that helps.
You can also experiment with reversing the hot and neutral connectors on the subwoofer power cord to see if that helps.
You may want to try running the plasma and/or the subwoofer on an isolation transformer to see if that helps
Here is some interesting reading..