I have this buzzing as well, mine went away when I moved it from one room to another. In the first room, none of the outlets are grounded, in the new room they are. I don't know for certain that this was the cause but I know that my TV now does not do this buzzing (It's was just as you describe, it changed with the brightness of the screen).
One thing to do would be to remove the back panel and then operate the TV. Locate the noise. If necessary, further fine tune the location with a paper towel tube to your ear or something similar. Once you locate the culprit, I wonder if it's some kind of coil whine (round copper coils which sometimes will vibrate at certain power loads, causing a hum or whine noise).
I don't know that this really helps you or not but I thought I would add the info.