Since the CRT working properly indicates the graphics card is ok,
I believe you may have a malfunctioning Controller board inside the LCD itself. While it could also be the LCD panel itself or Power supply (inside the monitor) your indications leads me to belive it most likely is the controller board.
I sincerely hope its still under warranty, but it probably wont be covered. You probably can get it fixed "relatively" cheap-at a guess in the $150 range but that is just a guess.
I think you should take it to a pro in your area and have him examine it to get a better idea of the problem, and cost to get it fixed but that by itself will probably cost about $75.00.