Does it fail to turn on altogether? Does it beep when you turn it on? Do all your fans still spin up when you press the power button?
If you have a spare video card, remove the current one, plug in the spare and see if it boots up. If not, it's probably not the video card that's busted.
If no lights, fans, etc. turn on when you press the power button, I'd guess a busted power supply (you can check if a PSU is good or not with a cheap PSU tester -
http://www.newegg.com/Product/Product.aspx?Item=N82E16899705003).
If it's neither of these, you're looking at a fried mobo most likely.
Generally speaking, if you don't hear your mobo's POST beep code (the little beep when you boot up a PC, one beep usually means everything is good; look in your mobo manual for further info about POST beep codes) and you're sure the mobo speaker is plugged in correctly, most signs point to dead mobo. If you get some sort of beep code, it's probably something else.
NOTE: POST will fail without a functional video card, but you should still hear some sort of audible confirmation. Same thing with RAM or CPU. If it's missing or defective, you should hear some sort of beep at the POST. If no beep - dead mobo.
EDIT: I'm glad to help if you have any other questions. I'll be back to check occasionally. I'm always lurking these forums anyway.
EDIT2: This is a fantastic step-by-step guide to troubleshooting power problems -
http://www.techspot.com/vb/topic53866.html