The more info, the better. As it stands, we can only throw out some guesses.
First, I take it this new computer has not yet successfully booted up once. The monitor is likely fine, especially since you tried with both analog and digital wires. Does the monitor have both ports, or did you use an adapter? Are you plugging the cable into the vga/dvi port on the graphics card itself, or onto a port built into the motherboard? When you boot up, do you hear any odd beeping? If so, have you searched online to figure out what the beep code is telling you?
Here's what I would do, given no more information:
I would open up the computer case (even if you're a novice) while the computer is plugged in but turned off. Frequently touch the metal parts of the computer and especially the power supply, and make absolutely sure that you are not shifting your feet around or rubbing anything at all (if you build up a static charge and fry your computer, you may not even notice that you have done so). If you are a novice, ever so carefully check to ensure that all visible cables are firmly plugged in. Do not press too hard on any cables (such as the cable running from the hard drives or CD drives) where they plug into the motherboard, but do a visual inspection to ensure they are plugged in fully and not at an angle. If you're not a novice, check to ensure that the CPU fan is operating properly and check to ensure that the GPU is seated properly. If there is an audio card, make sure it's properly seated as well. With your GPU, there should be a power cable plugged into it. If you have SATA HDD's, the power cables should be doublechecked, as those are a little easier to have partially unplugged than the older style.
If nothing seems amiss, make sure your video cable is properly connected and screwed into the video card. Carefully check the video cable, dvi or d-sub, where it plugs into the back of your monitor. On many LCDs, the cable comes in at a bit of an odd angle and because the cable is very stiff it is easy have it improperly plugged in, at least if you don't screw everything in completely. Even then, you may have issues, but with two monitors to test with you are not likely to have a problem in that department.