I don't think any Mac users have found that a cable like that works...the RGB (of VGA) to Y/Pb/Pr (of component) isn't a simple conversion...those few who have succeeded going component have had to use a relatively expensive transcoder, like this:
http://www.audioauthority.com/product_details/9A60
It's been a few years since I read of anyone trying, and I bet most just buy a newer, better HDTV, but, in theory you can use a mini DP to VGA adaptor connected to a VGA to component transcoder.
Personally, I'd sell the TV and buy a new one.