So I have had this cable for about 3 - 4 years and now the screen shakes a little and I have to readjust my chord to make it stable. Currently I have a XFX 5850 and I hook my computer up to a 42 inch 1080p samsung hdtv and I was wondering if an hdmi to hdmi cable would work better and prevent the flickering.
DVI and HDMI are exactly the same as one another, image-quality-wise. The principal differences are that HDMI carries audio as well as video, and uses a different type of connector, but both use the same encoding scheme, and that's why a DVI source can be connected to an HDMI monitor, or vice versa, with a DVI/HDMI cable, with no intervening converter box.
An HDMI to HDMI cable would have the advantage of being able to pass the audio signal from the 5850 to the Samsung HDTV. The DVI to HDMI cable doesn't carry an audio signal.