How do I get my Xbox banned?

call the police and file a police report

If the storage device with your profile on it was pinched too then phone support again and get an unauthorised access investigation opened. It'll lock off your account from use while the investigation is carried out and should give the police time to get your console back.

I already called the police - they have all the designated information. I already called tech support and they told me to come here and "request it on the forum".

Thing with banning a console is it's irreversible so even if you get your console back you're still down a few hundred quid for a new one anyway. Moreover there's no guarantee the thief will take it online so a ban for that console may be unenforceable.

If you have access to your XBL account I would recommend you go to a friend or family members house (whom has a 360 as well) and recover your account to their console then move it to a USB Flash Drive. Now your account is safe and secure with you. All you have to worry about is getting the console back and since you already contacted your local police department about it you are all set. Now you just have to be patient and wait for them to catch the thief.

If the only thing that was stolen from your house was your Xbox 360, games and accessories, and nothing else from your house, then you should be looking at friends, family and neighbors. People whom you have had in your house to know what you have. Most thieves will take everything of value, not just a gaming system and some games.