If you cannot boot up at all, I believe it's time to take it to your nearest Genius Bar for an evaluation - they have diagnostic equipment they can run and then tell you what appears to be wrong. It could be a graphics card issue, a screen or logic board problem. Is it still covered by a warranty?
FWIW, that would be a 27" iMac - there are only two models: a 21.5" and a 27".