I'm back online!
A few years ago, I got a new desktop computer. It was leaps and bounds over my old one, but for one problem - it wouldn't connect to the network. Now, I tried everything I could, and I exhausted the knowledge of a lot of other people, but in the end we resigned in defeat. For about four months, I had to leech off other people.
Then, while visiting the local tech shop, I came across a KVM switch, and for the next two years I used my kick-it-to-start computer for the Internet and my newer desktop for everything else.
Then, in August of 2008, that died, too. I was back to leeching off other people. After Christmas, I got a laptop computer (after only ten-odd years) in the hope the wi-fi would break the cycle. It works at the library, and it worked at my friend's house, but once again, not at home. I was getting quite peeved.
But, finally today, the problem seems to be solved. The router was reset to factory settings, and all of a sudden all the computers connected to it could access the Internet - i.e., the laptop. I imagine the desktops will too, but I'm not too bothered by them anymore.
And so, after three years, I can finally return to working from my room. The mystery seems to have solved itself.