Seems like your graphics card has just died...
I wouldn't keep my hopes up for it to get back working... If you can, try connecting an external screen to your computer, and see if anything shows up on that screen...
I think the computer's gpu burned out, and the computer isn't starting up because the BIOS is sensing the shock of power that isn't going thru the GPU...
I have a few questions.... A. When did this problem start happening?
B. What was the last thing you did? Where you gaming?
C. What kinds of things did you use the PC for?
D. How old is it?