You have to have a new download that might cost $$$$$.
And Halo 2 is only for original Xbox
[EDIT] Halo 2 IS compatible with the new Xbox 360s just not Arcade without a HDD. Although I'm unsure as well why you may have this problem, but I THINK it may be because of updates needed before its discontinuation from LIVE (?).
Ask any friends or search more somewhere else. Also (not trying to advertise) if you would like to play Halo 2 online when you can there are tunneling programs which can allow you to connect to other players around the globe through system link. Those are named "XBConnect" and "Xlink Kai".
Hope you get your problem fixed! :)