The vga to component cable should work. Here's another source:
It sounds like you have a resolution issue. I know my Samsung only supports certain resolution when in PC mode. (It has a vga input :) ) The problem is changing the resolution when you can't see what you're doing. Before I bought another piece of equipment, I'd try each of the different screen resolution options to see if any work. Set the TV to the component input you have the vga-component cable on. Double check all connections. Using a separate monitor, step through the options on the PC: right click on the desk top>properties>settings>move the screen resolution slider>apply>ok. Then switch the cable to the vga-component and see if the TV recognizes it.
Does your PC have a s-video out on the video card? If so, just use that. You may have the same issue but I doubt it.
Buy a new video card with s-video out. Cheap and easy to change.