I have a green port on my computer's sound card that I am able to plug headphones and computer speakers into. I have a stereo with component a/v input. Is it ok to solder 2 wires from a headphone jack connector to a component cable connectors and plug it in from my computer to my stereo?
I don't like paying the radio shack corporation $20 for something that they made for $0.05 in China.
Yes, it's ok. And if you have an SB Live or audigy i'd like to encourage you of using kX Drivers, which by default routes your front speakers to the rear (black) jack, 'cause it has better D/A converter and thus much better audio quality. And with good speakers you can distinguish the difference in a moment ;)
If there is a black port, use it. They are just... better than the green port.