You need a media converter box to go from VGA to Composite RCA or a higher end video capture card that also has RCA out.
Most people upgrade to a modern TV with VGA or HDMI and then connect via VGA or HDMI
Composite Video or S-Video are horrible.
Do you have any plans to replace the TV any time soon with a more modern or more featured model?
If you went the route of a media converter box, HDMI to RCA would give you the best quality. HDMI will handle video and sound and the media converter box would then patch that over to RCA Video + Left/Right Audio
Your computer would need a HDMI port though to support a media converter of this type.