It is unlikely that this will work. That is a passive cable designed for some laptops and projects which can either output (for video sources such as computers) or accept (for video display devices such as projectors) YPbPr component via their HD15 "VGA" connector. This is very uncommon.
This cable MAY work if your TV has inputs with RCA cables and you set your PC to output sync-on-green. It's usually not easy to turn this option on.
You can, however, hook your PC up to your TV via either RGB interface or the SCART interface (if it supports RGB, which most apparently do) using a suitable cable. The "RGB" interface is probably easier. What kind of connectors does it have? You can buy VGA to BNC cables pretty readily.
If this is an SDTV (not supporting HD resolutions), you will have to make your PC output suitable video somehow. You may be able to use the "Soft15kHz" utility if you're running Windows. Linux users can put a special modeline in their X configuration file. I have no idea what Mac users do
