|It sounds like a problem with your PC rather than the monitor. Does it happen under a certain set of circumstances, for example when the grpahics card is being put under strain by a game?|
The first thing I'd do is visit the ATI site and update the drivers for your graphics card. If that doesn't resolve it, try taking the side off your tower and, if possible, stand a fan near it so that cool air blows across the components. Run the PC and see if the problem persists. If it doesn't, you can almost certainly put it down to an overheating problem.
WARNING - if you're not familiar with the insides of a PC, don't go randomly sticking your hand in there, even if it's powered off.