I'm guessing that you know it's on and running?
Do you ever see an image at all? i.e. the post when it boots up, windows loading screen etc...
Does the monitor show you an error message after a while? Something like "no image detected" or similar?
Is this a new build or did you upgrade something recently?
Do you have another HDMI cable to test, or an flat screen TV or or other monitor to test with?