When you say 'display' . . . are you trying to watch a Netflix movie on your TV, or see the actual screen?
To watch a Netflix movie, I bought a cord at Best Buy (I think), but it goes out the bottom, the dock connector. That WILL NOT allow you to actually see the apps etc on your device, just watch a movie. But it worked great with my ipod touch.
I now have an iPhone, and got a cable that is an adapter, that accepts an HDMI cable, then goes into the dock connector. With that cable, you CAN see your screens etc.
I'm not 100% on this, but I think the cable you have only worked with an ipod that was called a 'video' ipod, that was made a few yrs ago.