Networking problems! DSL?

Ok, a friend of mine and I both play an online game called World of Warcraft. I would like to get a friend of mine on it and i have two computers at home so he could play on my other one. However, my father doesn't want me to download it on the second computer. My friend and I figured out that we could use a switch to network the computers together and use the shared files from the firts computer to play the game on the second without downloading it on the second. We did that and both computers have internet, but they cannot see each other in the network. And when i disconnect the internet they can see each other with minimal difficulty! I have tried restarting everything as well as taken down my firewalls and stuff like that. Does anyone know what the problem could be?