DVI-D to DVI-D should work fine with any DVI-D monitor(I have not seen a DVI-I monitor sold in, well forever).
Do you have another video card(or do you just have the onboard) installed in the system?
If you have other cables it may be worth testing out the monitor.
Does your monitor have multiple inputs? If so you might have to hit the source button on the monitor until it's on the DVI port that you have it plugged into. That motherboard also have a VGA output, if your monitor has a VGA input try that as well for trouble shooting purposes.
When DVI-D is connected, did you make sure to check the screens input. As the user above says, some do not auto switch.
If you have another device you may be able to test the cable. Having access to another screen and cable would allow you to see if the issue lies with the board it self.