As someone who has experienced similar screen issues (on three machines: old iBook G3, G4 and current Macbook), this is likely to be a main logic board problem IMO, & replacement of the board the solution. Apple may be sympathetic if it's our of warranty/Applecare (make an appointment at an Apple store if you can, be nice to the Genius etc.)
Video boards also fail, although you're more likely to get screen flicker.