This is a fairly simple question. Can I host/join a LAN game for minecraft if I have no connection to the main Internet? What I have is a router that can't be connected to the modem (I just don't have access to it. It isn't broken. ) and I want to be able to host a LAN game. Will it work?
Yes you can. Lan Games don´t need a connection to Internet. However, every player will have to play "Offline Mode". The LAN server will not enforce you to be connected to the internet to authenticate your account.
You just have to be sure that all computers have an IP address, by configuring a fixed ip on all machines, or by configuring your router to distribute those to all members of the LAN.