Black screen on iMac, system still running.

Yesterday I updated my mac to the latest edition, I think 10.8.3 or something like that. Then I downloaded and played Rollercoster Tycoon 3 from the App Store, all was working fine. This morning I went to take My iMac out of sleep mode by pressing the power button, my home screen popped up but only for a few seconds before going black. The system is still running, if you close it all down and then power it back up, I get the same, it only shows the display for about 3 seconds. The screen is totally black and after reading some other similar posts on here I cannot see anything on the screen at all. If I put it to sleep and then wake again my screen comes on perfectly, but only for 3 seconds or so.

My mac did have extended warranty on it, however that expired end of Jan.

Has anyone got any idea what the issue could be and or how it can be fixed and roughly how much it's gonna cost me???

Thanks