Those passive "VGA to xxx" cables are intended for the (rather rare) laptops that support composite and s-video output via their VGA ports. This capability is almost never seen on desktops. The cable simply won't work. The same applies for "VGA to Component" cables. These are usually intended for projectors that accept YPbPr component over their RGB inputs. They are again passive cables that won't work with PC outputs.
You can get an external device that will let you connect your PC to a TV. You have two options.
Option 1 is a device commonly referred to as a "scan converter". This will take 640x480p (and sometimes higher such as 800x600 or 1024x768) and mash it until it's something compatible with a TV (640x480 interlaced). Results are usually iffy at best, but it will get you a picture on a TV by any means necessary. This option is pretty easy, and the device usually costs about $30-50. The second link posted by SephYuyX appears to be an example of such a device. PC cards with onboard TV output are generally identical to this option in both technical operation and performance (i.e. picture quality).
Option 2 is to use any one of the common methods suitable for your setup (in this case, look for a little program called "Soft15kHz") to get TV timed video out of your PC in RGB as if you were going to hook it up to an arcade monitor. You then use an "RGB to S-Video" converter to get S-Video or composite (yellow RCA cable) to hook up to your TV. This avoids all the mashing and scaling. Results are usually decent but will depend on the quality of your TV. With a high quality TV and an s-video connection, results can be nearly as good as an arcade monitor, but there will usually be some overscan that can be impossible to adjust out without access to service mode. This option is a little harder, but the results can be quite a bit better. Cost for the device is again about $35-50.
Composite video will always look bad. You should use S-Video if possible. Component YPbPr connections can offer identical quality to native RGB inputs if available and the conversion from an RGB source is done properly. The only off-the-shelf device I'm aware of to do this conversion at a reasonable cost is the JROK device, and it wasn't cheap last I checked (~$100+ship), but prices have since been removed from his website.
It sounds like you have an adapter of some sort in mind, but I don't see a link. If you post a link to the device you have in mind, it may shed some more light on your situation.