Here is my problem, I have a 360 hooked up to a newly bought hdtv, unfortunately, I do not have a proper surround sound system for it. I do have though a surround sound speaker set for my PC, it uses the green, black, orange connectors, 5.1. The pc is in the same room and very close to the tv.

Now then, my question, can I take a TOSLINK cable and connect from the 360 adapter thing and plug it into the TOSLINK "IN" in my computer's sound card, and then send the signal from that through the same sound card to my surround sound speakers which are plugged into it, and finally achieve true surround sound?

It probably depends on the capability of your sound card. Get a cable and try it.