Usually, the biggest problem people have with the cable is not giving it a few seconds to let the authorization chip do it's thing:
1. Put the TV on the correct input
2. Connect the iPod while in a Menu, not playing anything. Be sure to connect directly to the iPod, and not through any Docks or any other accessories.
3. Wait five seconds.
4. Now play the video.
If the iPod screen goes to a "music-like" now playing screen with the album-artwork displayed, it is correctly outputting the video, and you might just have the other end of the cable incorrectly connected.
If the iPod screen says "Connect Video Out Accessory" or something like that, then there either isn't a good connection established at the docking port or there is possibly something wrong with the three hardware components: TV, iPod, Cable.
There have been reports of certain TVs not working, and I believe this is because most TVs with HD/Component inputs send a connection signal back along the cables, but some don't. The iPod AV Cable and the authorization chip rely on this connection signal.
Anyway, I hope this helps.