Check for hard drive light activity. If there is activity (not just a stuck on or off light) then there is a chance that the onboard graphics processor went bad--of course, that assumes that you are connecting your monitor directly to your motherboard, rather than a separate graphics card. Try another video card in the machine and see what happens.
If you have a separate video card in it, try removing it and connecting directly to the motherboard--this will of course depend on you having an IGP (Integrated Graphics Processor).
If you have no hard drive activity lights, try removing every expansion card inserted, unplug your hard drive, cd rom drive, disk drive, and remove all but one stick of memory. If nothing comes up, try the other stick(s) of memory individually.
If still nothing, do a visual inspection. Are there any capacitors with raised caps? For an explanation of this, check here: http://www.pcstats.com/articleview.cfm?articleID=195
I hope this helps you.