JTHM, I'm sorry, and I guess I better clarify that page. I use that wireless card only as an example, and also because, in that ONE particular case, that particular card is hard to determine from lpci. Don't worry about that part. You did fine in giving us information.
That SiS card was what we were interested in anyway, just to make sure it wasn't some unusual card.
After that brigame's questions are good ones. If possible, swap a cable, try a liveCD of some other distro to see if it sees the card, if there's an MS installation on there, see if it can reach the router.
The issue here is to try to pinpoint the problem. Is it the O/S, card, cable or router? The questions brigame asks can help figure that part out.