these kind of problems are probably the hardest thing to solve without having access to the computer, at least, it is for me. So far, I haven't been able to fix things that way.
Now, Win XP includes a built-in firewall. I don't remember where you access it, but make sure it is disabled. You mention your friends have disabled their firewall, but it could be an external one, so tell them to check their default one.
One of my friend installed a router and since then has lost internet access

He is anxiously waiting for me
A few things you could try, is to connect to the internet without the router, i.e. no network, but a simple computer hooked to one internet connection. It could be your network protocols, so doing this will ensure a "clean start". If you can connect to the internet, than try to network your computer with another directly, without anything else in between and make sure you can share your files.
From then, you evolve. Make sure you have the appropriate network protocols. You will need:
- Client for Microsoft Network
- Network Card (Realtek seems to be the best cards available and they don't cost much)
- NetBeui (binded with the next one and with Client for MS Network)
- File and Printer sharing for Microsoft Networks
- TCP/IP (binded with Client for... but absolutely not with File and Printer sharing)
- IPX/SPX (or whatever it is called
) can still be useful for some MP games but I don't think it is necessary for now. Once everything is working, you can still add it.
I'd say start with minimum config. Take #1,2,5 to get hooked on the internet, than remove #5 and add #3 and #4 to see if the network is working, than if everything goes fine, add#5 again and then add your router and try the network and the net connection.
You have to keep in mind that it is quite possible your router or one of your cable is defective. Following this step by step procedure for each computer of the network will ensure you that it's not the case (it's a pain in the b***, but it's the only way I know when something isn't working).
That's all I can do for now... Check this, and post your results. I might have other comments/things to try when I get your feedback
