S-video is basically y/c seperated video signal (you can buy or make a convertor to recombine the components to form normal 'composite' video signal).
Zionworx has nothing to do with the connectors on the back of your machine, it just tells windows to use the second output device.
Now your problem maybe as abvious as wnp suggests, or it may be one of the following:
1) It may be that your video card does not support dual display output; that is, it can only output one desktop (albeit possibly through two outputs - the vga and the s-video). This is called screen cloning and is common on a lot of more basic model graphics cards. Please give us details of your card, OS, and driver versions - so we can help you.
2) You may have only basic drivers installed. Some drivers which often come as part of windows will only allow the more basic features of a card, essentially neutering the capability you are after. Try getting the newest drivers from your graphics card manufacturer.
3) The lead might be crap (like wnp suggests).
4) Your TV may not be picking up the signal. Now this can happen for a couple of reasons. A) you havn't selected AV (like wnp suggests). B) Your tv and video card maybe 'too clever', often a device such as a TV will wait for a signal before it switches into AV mode, when you couple this with a graphics card that waits for a line to be connected before outputting video - you get a right old mess and have to find a way to jump start the process.
5) If your using a laptop you will need to 'toggle the output' this is usually done by holding the option or alt key and tapping one of the F keys with a symbol of a monitor above it.
6) You may have to switch from composite to s-video is in display properties (right click the desktop) under settings and advanced on some video cards: I've seen it on some Ati drivers.
7) It maybe something completly different which I havn't thought of yet - post up anything you find - it'll be helpful to the next poor individual who has the same problem
Incidentally, in your post you aluded to your TV not having video component support. If your TV has a SCART input then you can buy a Scart Break-out cable which will give you all the individual phono conectors (including audio Left and right in and out and video composite in and out).
kind regards
Diceman