Any time you have prolems with video output, the first thing you should do is check that your video cable isn't lying close to the power cord for any length. the EM field is enough to screw up the video. Most often it causes ghosting and shuddering, though.
But if it's happening with specific sites, it might be because they're too much of a specific colour and your hardware is having trouble keeping sync'd. To test this, make your browser windowed (non-maximized) then keep making it smaller until the video locks. If it never locks, I'm out of ideas.