heh... it would be rather challenging to see the bios screen without video, now wouldn't it
well there's a few things that could cause it:
1) dead hardware
2) something's not seated properly
3) incompatible hardware
first off, are you getting any error beeps out of it?
first thing you should try is clearing the CMOS. I've seen several mobos that don't work out of the box, and clearing the CMOS (which clears bad hardware settings) fixes it.
also, double check all your mobo jumper settings. in particular, sometimes there is a jumper for locking the FSB to 100MHz or something, and sometimes it comes set that way, which could cause it to not boot.
if that doesn't work, try removing and reinstalling the CPU and RAM.
if that doesn't work, try removing the RAM entirely and see if you get any different signs of life.
If you can, try switching RAM and/or processor with a different computer. if the CPU and RAM work in another computer, then at least you'll know they're not bad... and if the computer still doesn't work with known working CPU and RAM, then you narrow it down to the motherboard...
If you have one, try an actual video card. It's weird, but some motherboards don't want to default to on-board video, sometimes you have to use a card to get it into bios, then switch it to on-board, then remove the card.
Do you have a hard drive connected to it? if so, when you boot it, do you hear hard drive activity? That's a good way to tell if it is simply not outputting video, or if it's not booting at all... if you hear hard drive activity then chances are it's just the video that's not working, which is a bit easier to fix than getting no signs of life at all.
MOST of the computers I have built have had initial booting problems, and all the things listed above are the stuff that generally takes care of it. I have only had one mobo that didn't work even after all that, and that was because they connected all the standoff locations on the board to one of the voltage rails, instead of ground, so by using metal standoffs instead of plastic (it didn't come with any so I used what I had) to connect it to the (grounded) metal case, it killed it.