Do you have a dedicated graphics card? Try using another port on that card to plug your monitor in or remove the card and try the on-board graphics, if the problem still persists, try another monitor, replace whatever is not working for you.
Also, another option is to use a different power supply for your monitor in the case that your monitor has an external power supply. (be sure you're using a correctly rated power supply to test it out though. AKA right voltage and VA rating)