Well you can check if the backlight/LCD or the video card died; just plug in an external monitor and see if it works; if you don't have an external your only shot is to check out the Apple Store.
I just got mine back from the Apple service centre. They had to replace the logic board. This problem looks to be spreading. I would get it to your nearest Apple service place soon.
I could connect to mine by using screen sharing from my old iMac G5. It worked fine just no screen.