It's the Displayport input on the monitor. I had exactly the same monitor and exactly the same problem. Don't forget that this monitor was a couple of years old when you got it too. And yes, your motherboard does have a little speaker on it, it's just not beeping because there's nothing to beep about, as far as it's concerned your PC is in tip-top condition. See if you can find another monitor with displayport to use for a few days just to be sure, but that's 99% the cause.
EDIT: Also, try using HDMI on the graphics card, should work fine then.