My guess would be that you're using a DVI-A (analog only) cable, but the monitor requires a DVI-D (digital) signal. Or perhaps the card is not sending the digital signal over the digital pins in the DVI-D connector... instead only sending an analog RGB signal over the analog pins. In either case you'd get no video if you connect the cable to a DVI-D (digital only) DVI monitor, but would get video if you use a DVI->VGA adapter to extract the analog signal from the DVI connector and send it to the monitor's VGA input.
If the former, then buy a DVI-D (digital) or DVI-I (digital + analog) cable. If the latter... um... not sure how to fix that. Driver options in Control Panel maybe?
Pictures of the different types of DVI connectors can be found
here.