3.5mm headphone jack -> component video?

3.5mm Jack can be a bit strange. If you noticed, some of them have different numbers of black stripes on them. 1 stripe for Mono-Audio, 2 stripes for Stereo-Audio, 3 stripes for Video + Stereo-Audio (rare, and usually usable only for specific devices).

I had one with 3 stripes for my D90, which enables direct playing of Video / Images from the camera directly to TV (the other end is RCA jack).

Although the physical cable supports transmission of Video Signal, but normal headphone jack on your PC/Mac will only supports sending Stereo-Audio as they are designed for.

The cable has a third terminal on the jack that is for a video signal. I have the same thing and use it with my Zune whenever I'm traveling or at a friend's house. Your audio port on your computer is likely not going to have a video signal coming out so video to a tv will be the s-video or vga route.