Chances are that your cable isn't supported by the version firmware that your iPhone is on. Most AV cables only work on firmware 3.1.3 and below.
If you're phone is jailbroken you can go to Cydia and install Resupported 4 and that will allow the firmware to support your cable. Resupported 4 is $3.99 on Cydia but comes with a 10 day trial version. DO NOT install the cracked version of Resupported 4 because it does NOT work and has been causing some peoples phones to lock up.
Resupported 4 will allow you to display your videos, youtube, and most video/movie streaming sites to show on your tv. If you want everything from your springboard, including most apps and games, to show up on your tv you will also need to install an app called TVOut2 Mirror TVOut. It's also in Cydia and it's free.
If you're phone is not jailbroken then there's really nothing you can do except return your cable to where you purchased it.