I too had this problem but I found a solution. My noise would even change as I moved the curser around.
I did a lot of searching around but ended up finding the solution by accident. The problem, it turns out, didn't have anything to do with my screen. It was a fluorescent lamp plugged in to the same circuit as my computer. It was actually on the other side of the room but it creates interference in the AC power that conflicts with the power supply in the computer. Somewhat similar to what makes some car stereos buzz when driving.
I have played around with it since and changed my desk lamp to a CFL bulb and even though it was plugged in directly beside my computer it didn't make the noise. It turns out just some fixtures do it, and from what I can tell, ones with a dimmer switch are the worst. So, I would check to see if you have your computer plugged into an outlet that is on the same circuit as a light. Even an overhead light such as above a dining room table. It sounds weird, but it depends on how your house is wired because that light doesn't even have to be in the same room.
Surge protectors may help but unfortunately you may have to go to a more expensive current modulating power bar like the ones made for high end stereo equipment.
For me, it was just a matter of moving a lamp. I hope this helps someone out there.