Well hell, while were at it. Might as well through in the PSU. A dead or dying power supply unit can exhibit similarly described symptons. In fact now that I think of it, it could be...
Dead ram .... computer won't turn on
Dead mobo .... computer won't turn on
Dead PSU ..... computer really,really wont turn
Dead CPU ...... computer won't turn on
Dead display adapter ... computer won't turn on
Power Switch is broken ... computer won't turn on (+you feel like total dumb ass when you discover this is the reason why)
Dead harddrive ... computer won't boot but it'll still display some stuff
Dead chipset on mobo ... this is a little more subtle your computer might pretend to turn on depending on what chipset it is then seise to work. the end result? ... computer won't turn on
Shorted pci device ... computer won't turn on
Shorted (but still working) PSU ... computer will turn on after being turned off for a variable number of seconds
I mean this might not quite be the comprehensive list. But you can get a general feel for just how screwed your situation might be.
Ofcourse it might be of small use maybe to tell us what your computer does when you attempt to turn it on. Does beep at you perhaps? Are you able to even access the bios? Do you hear any fans turn on? Is your CPU warm to the touch when you temporarily cut off the fan? Does the power button do anything at all? Do the lights in you room flicker just a little when you turn it on? Is there a burning smell coming from it?
Are you near a fire exstinguisher? Can you get to safety?