Right, let's see if we can put an end to this
As said earlier, VGA => S video dongles don't always work, in fact in my experience unless they come with the video card I'd go as far to say that they're far more likely NOT to work than otherwise.
The reason? Quite simply, this requires specific support from the video card. The signal sent over a VGA cable is nothing like that required in a composite specification, it's impossible to convert one to the other via a simple dongle. The video information is split over lots of pins, the timings are all different and as you'll need a box of electronics to switch it all over - not just a change of connector.
So why does it sometimes work then? Well, not all the pins on a VGA connector are used, so sometimes video card manufacturers choose to output composite information on an unused pin. The dongles / adapter leads just connect the composite / s video connectors to these formerly unused pins, which stream the correct video data.
So as you've probably guessed by now, if you connect one of these dongles to a normal video card, it won't be pushing anything down the pins the adapter is wired to, and as such your TV will display nothing. Sometimes there's a setting which enables the output down these pins rather than just having them active all the time, but it sounds to me like if it was there, you would've found it by now.
So, is there a reliable way of doing it? Of course, but you'll need to spend more than a simple adapter lead. You'll need that box of electronics to convert the signal that I was talking about earlier - and such boxes are called scan converters. Have a Google around, there's loads on the market - but I'd advise staying away from the really cheap ones since they have a habit of noticeably reducing the picture quality. Once you've got one though, you can just take the VGA output into the scan converter, and the S video output out of the scan converter into the TV - no hassle, and that's a reliable setup. If you connect it up as I've described, make sure the TV is set to the correct input and the laptop is set to output to the VGA port, that's pretty much guaranteed to work (obviously unless you've got a faulty component along the line.)
Hope that helps!