A friend of mine has a similar situation. He has a TV next to his monitor, and whenever the TV is turned on, the monitor starts shaking. Turn the TV off, and the monitor is rock solid.

We think it's some sort of shielding problem. We tried putting a sheet of metal between the two, but it didn't seem to help.

The monitor is seperated from the TV by an isolation transformer which should block any RF through the power lines.