I do have another internet in my house and i switched my connection to the wireless one, which still fails to work. I must assume that it is a system problem

This seems like a quite simplistic solution but be sure that you actually downloaded the correct game version. The one designed for the mac. If that is not the issue you may have some kind of issue with logging in, in which case you should try to reset your password.

I have 2 routers and I am running the correct version AND I have the mac version.

Okay, we've established that everything on his computer is fine. It's just something is wrong with sending outward connections. There is another way to log in. Go into the game and type in something like "/login <username> <password>" into the chat box. You can do this is single player or multiplayer as a guest. If the syntax isn't correct, tell me and I'll look it up.

I can play single player, but I do not know how to play multiplayer as guest.

Just click on the multiplayer button on the title screen. Choose a room and connect to it.

Cant it just tells me to log in.

Try going into single player mode and entering the syntax I provided to you earlier.

It tells me the command can only be used in multiplayer.

try /join, the command you used might be an operator command.