I'm no expert but here is what I found:
- Composite AV cable only works on the TV with video aware apps on the iPad. The app apparently controls whether video output is sent to the dock connecter or not. From what I can tell, both the video app and photo app in slideshow mode do send a video signal. There might be others but it would be on an app-by-app basis. The composite AV cable does not provide mirroring. It just sends an output signal through the cable to the TV. The iPad screen changes to a message indicating the output is being shown on the TV.
- Some people have reported the same problem you are having...audio yes, video no. From what I can tell, the most often cause is a defective cable. Mine gives me both audio and video so I have not experienced the same thing as you. If you are in easy reach of an Apple Store, take it there and have them try it out.
- If you want mirroring, where the TV shows everything on the iPad, you need the Digital AV Adapter, which allows you to connect a HDMI cable to your iPad. Of course, you will also need a HDMI cable. This provided video and sound and everything on the iPad is mirrored. Works quite well.
- I also agree with many others on this topic - way too confusing and not consistent with the simple, easy Apple experience.