I built a PC in 2009 and had a similar problem. I bought a new monitor that arrived before my PC parts did. I plugged the monitor into my old PC because I wanted to check it out, and was using the new monitor until the other parts arrived.
I built the PC and everything seemed fine. Fans were running and everything. But nothing would display on the new monitor. I finally plugged in my old monior and everything was fine. I loaded Windows and everything. I plugged my new monitor in and there was no image.
Finally, I put my new monitor aside, unplugged, for a couple days. When I plugged my new monitor in now, it worked no problem.
I was never able to find any explanation to this. All I can think of is that plugging the computer into a really old PC with a different connector somehow configured the monitor to work with that connector. Leaving it unplugged must have reset the monitor to factory condidtion.
I don't know if this is your problem. But before doing a ton of work, try using a different monitor, and try using different type of connections (displayport, HDMI, vga).
If this doesn't work take out your graphics card and plug directly into the motherboard. Read the instructions for the graphics card installation. Maybe you need to install drivers first for it to work. To do this you will need to plug into your motherboard and install Windows (or whatever you are using), then install the software for the graphics card, then physically install the graphics card. It's also possible that the graphics card needs to be physically installed before the software, but even if this is the case you will still need to plug the monitor into the motherboard and install the operating system, then the graphics card software. You have to read the graphics card instructions for the proper installation procedure.