Are you connected to the correct HDMI port on the Samsung? You may need to change the TV's menu to recognize the input being from the HDMI port you plugged into.
You may be able to try plugging the dvi-hdmi cable into another system to see if the cable works but the setups must be identical to really demonstrate that the cable is good.
Check your graphic card's output specifications to the TV's input specifications. There are different types of DVI (dvi-a, dvi-d, dvi-i) and the connectivity must match.
Dell's website may provide some specific guidence via the model number of your Dell PC. Likewise the website for the graphics card.