Computer boots... but shows nothing. What do I check?!?

My roomie wanted to buy a new computer, so I went with him to buy one. After much deliberation, we decided to build one of our own.

I have built three machines and have successfully booted them all, and they've all lived happy and productive lives. Which is why this problem burns my cookies.

I got everything inside (Installed Motherboard, installed Processor (Intel Core 2 Duo), installed RAM sticks (2, in a pair, for total of 2GB, both in the "blue" slots, as per the manual), plugged up all the buttons and such, installed the video card (A Diamond ATI Pci-Express x16 card), added the hard drive and the dvd burner (serial ATA, as per manuals). Closed the sucker up and booted it. It came up, ran for a few seconds, went down. Came back up and continued running. However, no video ever appeared, neither on either of the two VGA monitors I hooked up, nor via the HDMI + DVI cable I hooked up. It comes up and stays up. It never beeps. And it never shows video. What to do next?

Computer boots... but shows nothing. What do I check?!?say yes

Sounds to me like you have a bad video card. From what you posted it seems like you checked everything. Do you have another video card (maybe one from working system) that you can swap it with. The idea is to use systematic troubleshooting. Replace one component at a time until you figure out what the problem is. However, if you are getting no video it has to be one of 3 components, the video card, the processor or the memory. The rest of the stuff wouldn't cause this problem... also I doubt you actually need a keyboard as most new motherboards don't require them to boot. Hope this helps and good luck.

P.S. Two other thoughts... 1) it could be the power supply not supplying enough power to all the components, or 2) it could be a heat issue with the processor (did you use thermal paste? and did you make sure the fan is blowing the right direction on the heat sink?)