A MONITOR that supports only HDMI but not DVI? are you sure it is not a TV?
Does it support ONLY HDMI or is it that it has HDMI as well as DVI? if so then connect DVI to DVI.
If it is a TV then know this:
DVI to HDMI causes significant quality degredation. DVI to HDMI is meant for a few rare HDDVD decks that came out with HDMI output but a DVI plug... conecting a computer through one of those cables does NOT work properly and causes you to have vastly reduced resultion. I researched the heck out of the subject and actually tried all the solutions. Trust me on that one, get an HD dongle for an HD out capable video card (geforce 7 and above, ati 2xxx series or above if I remember my ATIs correctly). The dongle will have component output which is how you want to connect it. It will look way better then DVI to HDMI cable. (they make DVI to HDMI conversion boxes that actually convert the signal, but those START at 200$)