Phantom wireless network!

Hi. I'm not really sure what piece of hardware or software is causing this problem, so this may not be the right place to ask, but here's the deal:

I have a wireless network consisting of a Linksys WRT54G (The one pretty much everyone has), a PowerBook, a Dell laptop and a wired iMac G4. A month or so ago, the wirelessly connected computers lost their ability to connect to the internet. I ended up reseting the router and starting a new network with a new name. After I reset the router, however, I noticed something puzzling. The old network was still showing up!

Even with the router unplugged, the old network shows up in the list of wireless networks on both the Macs and the PC. This persists even after restarting the computers or turning wireless off and on. I'm able to connect to it, and it shows full signal, but will not connect to the internet. It appears side by side with the 'real' network, which works fine.

I can only think of two explanations for this, either I somehow accidentally set up a computer-to-computer network on one of the computers, under the same name as the old network (which I find quite unlikely), or that a third party is spoofing my old network.

The phantom network isn't causing too much of a problem, although my PowerBook keeps connecting to it by default instead of the working one, but it does have me pretty confused, so I was wondering if anyone had a clue as to what was going on.

Thanks,
Zweben