I have my PC and my X-Box upstairs in my room. My internet is wireless from a router on a computer that's downstairs. If I run an ethernet cable from the X-Box to my computer, will I be able to play Live? Or do I HAVE to get the wireless game adapter (80-90 bucks)?

You should be able to do it, though it may require some work. Please see this thread, as you are essentially wanting to do the same thing.

Thanks!