Start with the obvious first. Unplug everything except for the power, keyboard, mouse, and graphics. Make sure that there's only one cable going from the graphics card to one monitor. Ignore any other monitors for now.

Double check the graphics card's power connector, and make sure that the PSU can handle the card.

Turn the computer on and see what happens. If it still doesn't work, shut it down and move the cable from the graphics card to the onboard graphics and try again.

If that doesn't work, turn the power off and disconnect the power cable. Double check that the RAM is in the correct slots. It will probably need to be in A1 and B1, for example, and some computers won't start if it's in the wrong slots. Double check that the motherboard can take that RAM at the speed printed on it, and that it's on the motherboard's compatibility list. I've had RAM cause these symptoms when the motherboard didn't like it.

If it still doesn't work, then come back here and post your full specs. Let someone double check that everything works together and that there are no compatibility issues.

Good luck :)