The reason why that little cheap ass cable exists is because there's special graphics cards that allow composite and s-video to be transmitted through the VGA port, it's not a normal VGA connection on television sets or computers.
VGA is Red, Green, Blue, Horizontal Sync & Vertical sync, grounds, and data signals going down 15 different wires.
Component is the luminance signal (Y) and the colour difference signals (R-Y and B-Y) being carried down 3 different wires.
S-Video is The luminance (Y; brightness in an image) and chrominance (C; colour) information carried on two separate wires with two separate grounds. 4 Wires total.
Composite is the luminance and chrominance signals being combined and sent down one wire and one ground, 2 wires.
Again, two entirely different signals you can't just plug a wire in and expect your TV to know what you want it to display, you have to have converters with microprocessors and video encoders or decoders to achieve this.
Since your TV has no S-Video input, just use composite. Converting S-Video to composite will yield the same results. Remember these systems were designed for low resolution CRT's in mind, so when you go to a modern high def set, every single imperfection of the lower grade signals (S-Video, Composite, RF) will show up, so it's best to start with the best possible signal you can get which is RGB to get the best possible signal on a modern TV.