Does the PC make any beeps on startup (even though nothing appears on the screen?) - If it does make several beeps, count them and look up the manual for your motherboard in your PC. It should pretty much identify the part its having a problem with. If your PC does not make any beeps, there are several likely suspects being the RAM, CPU, Motherboard, Graphics Card or PSU. If nothing untoward happened to the PC before it stopped working (like it being knocked for example), and the fans are all still running then it is likely to be the RAM or Graphics Card. If the fans in the PC arn't runniing, and it isn't obvious that it is running when you switch it on then its probably the PSU. I doubt you would have, but if you have some spare parts like another graphics card, ram or psu, try swapping them and seeing if it boots up with that in place. If you don't have any spare hardware, try going along to a local pc hardware place and ask them to diagnose the problem (not sure if they still do this or not).
If they are a decent place, they should test each of the major components out and let you know what the problem is. Saying that though, once they have diagnosed the problem they probably will expect you to buy the component from them to get it fitted.
[EDIT] Just as an after-thought, depending on whether you are using a DVI or VGA cable, most graphics cards these days tend to have 2 outputs. If this is the case, try plugging the cable into either (which I am sure you have already tried if available) to see if it makes a difference. Also, try a different vga or dvi cable to see if it is that which is at fault.