I have come across this once before.
Long story short.. I finally realized it was the dvi cable from one monitor. Two of the pins in the dvi cable had somehow got bent just enough to touch. So when I plugged it into the graphics card, it shoved two pins into one hole on the graphics card. This caused the pc to not respond. I took a paper clip, straightened out the pin, then carefully reformed the holes on the graphics card. Take a careful look at the graphics card holes, see if it's mis shapen, and check the end of the dvi cable for bent pins.
I was building a batch of Radiologist pc's at the hospital I work, very high end, very expensive pc's. Costs about "mid-range car" expensive pc's. I had built a test bench with only the one set of monitors on it, then built each of the 7 pc's off of that rig. Came down to the last two and suddenly they won't do anything. I then swap back to the original pc's, and suddenly they won't do anything either. As I stood in front of a batch of pc's costing roughly what my house does, I realized the only common denominator was myself, and the monitors.