IPv6 Connectivity is unlikely to return anything unless you're using some semi-futuristic networking hardware at the moment (lit: you're a nerd who can afford an expensive router xD). The IPv6 thing isn't a problem. When you're playing the game, have you tried alt+tabbing out and looking for a Windows Firewall alert? That's something which I forget to do almost every time I play a new game, but it's vital. Try that and see what happens.
Also, some games are just naturally picky over LAN, in my experience. Make sure you're using the same versions of games as the other people on the LAN, try restarting, try using the Ethernet connection to the LAN instead of wifi (playing games over wifi's a bad idea, I find, because it has high latency and loses packets).