I have the new 6-core, 16GB ram (2x8GB) and 5870 card. My monitor is a 30" Dell WFP-HC with dual-link. Randomly, I get a noisy screen (snow) that can only be fixed by shutting the screen off and back on, or unplugging.
I have had that symptom with a 2009 mac mini hooked up to a 720p hdtv via hmdi/ hdmi-dvi adapter. a wiggle of the line/cable has sent it packing. There is a chance you have a defective cable. or a defective connection right at the jack of the screen.