If you have a different monitor, try that one and see if it will work. If it doesn't, you might be screwed since you need a monitor to fix most problems.
Make sure the video card is securely plugged into the motherboard. It could be that it's in enough for the lights to come on but not let the monitor work. I've seen this happen.
If that doesn't work, you might try a different video card.
Does the computer have a built-in place to plug a monitor in? I know you said you built this one, but I'm just throwing ideas out here. If there is another one and it works, you may need to disable the drivers for that one and install enable the drivers for the other one.
Let us know what you come up with.
Ok, so I just finished getting my part's yesterday for my new computer the other day and began working on it this morning. The only thing's I'm keeping off my old computer was my HD's (2 SATA), DVD drives, and PSU (Antec Neo 450w). So i went ahead, pulled out all my old part's and began to throw together my new computer. Well, to my demise, everything seemed to work other then the moniter! So for the last hour I've been searching around trying to find why this is happening, and I can't find anything that helps. Anywho, time for the part list!
Case: Antec P180 Advanced
Processor: AMD64 X2 6000+
Video Card: EVGA e-Geforce 8600GT Superclocked
RAM: Crucial BallistiX Tracer 2GB PC2-6400 Dual Channel DDR2 Kit w/ LED (2 x 1GB)
OS: Windows Xp Home
Now as for my moniter, I KNOW it works, it's only about 2 months old and I just tested it on my laptop. But when I connect it to the video card, it doesn't work for some reason! It seems as though everything from the fans to the harddrives run, even the fan on the video card works, but I dunno, it confuses me xD