Is it a high speed 1.4 cable or regular? What brand is it and how much did you pay for it? It could be a crappy cable...
Also, there's probably going to be more to it than just connecting the cable... like reading the manual. You'll need to fool around the monitor settings and change the input from VGA to HDMI or HDMI to DVI (yes, even though it's connected via HDMI. DVI is also HD compatible). My point is, read the manual and see what you can find.
In the input>edit menu set the mode to DVI.