The computer does not boot up a tall
You'll have to include more information. Model number of the motherboard, if the computer beeps when it turns on, if so the pattern of the beeps.
From what you've stated it could be plenty of problems. I'll list a few things from simplest to most difficult for you to start with.
First make sure that everything is firmly attached to the motherboard... power connection, data cables, memory, heat sync and processor... often a loose connection will be the problem.
If you have multiple RAM chips installed, try removing one - a faulty RAM chip could also prevent a computer from booting in some cases.
If it still doesn't work, try disconnecting ALL the data cables and the power lines for everything except motherboard and video card (if your video card has a power cable attached, that is) If the computer turns on, the most likely problem is that one of your hard drive or CD-Roms is IDE, and the connection is backwards.
If that doesn't work, remove the heat sync and fan over the processor, and make sure that the thermal paste isn't rock solid... (usually a white substance that helps transfer the heat from the CPU out) If the thermal paste looks cooked, go buy a tube of it (pretty cheap, you can get it at any computer hardware store) and replace it. Make sure you take off ALL the old paste from the heat sync and the processor before applying a new, uniform layer. Unfortunately, if the thermal paste wasn't present, or was very spent... it might've fried your CPU... not likely in newer computers however, since motherboards have heat sensors designed to shut down the PC before any harm comes to the CPU, so don't rush out to replace the CPU just yet.
If it STILL doesn't turn on, the problem could be in your power supply, or on the motherboard itself. First look the board over carefully, to see if anything looks melted, charred or somehow deformed. If so, you're probably better off replacing the entire board, if not, your problem is either the power supply itself, or you've fried the CPU.
Hopefully one of these helps with your problem, if not get back to me with more information.