This is easy. First of all, the new BC update that you will be prompted to download will MOST DEFINATELY fix the odl one's mistakes. Honestly, the only problem with the first one wasa 16:9 hud fuck up, which really wasnt shit to begin with (I have a 16:9).
As soon as you start emulating an XBOX (original) game (halo 2 in your case) you will be asked to download the backwards compatibility list for December. This one is the fix, so get it.
Now, try online...if not, then take out the disc and sign into your account via the 360 dashboard. once you're logged into live on your controller, put the disc back in and it will work. Since, however, halo 2's user accounts are not 360-unified you will have to chose your character just like the old days and then sign into the appropriate xbox live acocount (if you have more than 1 XBL acc registered on your 360. I happen to have 5 XBL accounts on mine.).
Good luck bud.
-t