You need to forward the required ports for mw3 I don't remember what they are, logon to your router and use fort fowarding option. If you still don't tell me what your router model is then I can help you forward the ports.
If you are banned then it must say VAC ban record on your profile, if it cannot connect to online services it might mean :
1) inappropriate behaviour in game so they usually ban for a max 3 days but there is no way to check that.
Also if you are banned it should say cheat detected when you start mw3 so Idon't think you are banned either forward your ports or wait 2 days and then try playing see if that works thT usually works for me because it has happend to me before.
This link might help you if it doesn't work then email me then I can pm it to you.