Going S-Video to S-Video is probably best.
http://www.amazon.co.uk/Philex-S-video-1-5m/dp /B0009HC4NA
That may be what you want -- do both of your S-Video ports have 4 small holes?
I'd buy from a local electrical store -- Maplins or Radioshack are good. Hopefully they'll let you return if it you see that it's definitely wrong.
As above say though, it'll only carry video. Do you have two phono ports for sound (perhaps white and red coloured, labelled L and R)? If so, these will take sound, and will hopefully work when using S-Video too.
You can get a headphone (3.5mm jack) to phono cable from the above shops too. Your cable you took a photo of is one of these phono cables, with phono connections on both ends, so you could get a phonon to 3.5mm adapter if the cable you have is long enough already (and isn't damanged).
If possible, check the instructions on your TV. The manual should let you know what connections to use for audio when you're using S-Video. Failing all this, there should be a yellow (I think) phono jack next to the white and red ones. This is for video. A S-Video to phono cable should be available (again, with the addition of another cable for sound).
http://en.wikipedia.org/wiki/S-Video
Note for all this: S-Video is an analogue connection. As such, timing signals aren't properly in phase with the signals, and it can only carry SD (480dpi vertical or so) resolution. So, it won't be nearly as good as your laptop's screen. It may suffice though.