[quote name='sellerr2d2']
Any way, is there a way to download XBOX LIVE games or themes to a USB drive and then transfer it from USB to the XBOX 360?[/QUOTE]
The game either needs to belong to the console or the gamertag for it to work. I assume you can't assign anymore licenses to the banned console and you wouldn't be able to sign in on that console anyway.
Here's an example of how it works. We have two Xbox 360s in the house, Xbox A and Xbox B. Trials HD is sitting on the hard drive of both consoles, however, the license belongs to Xbox A. Anybody can play the full game on Xbox A regardless of who is signed in. You do not need to be connected to Xbox Live. You can play offline. In order to play the full game on Xbox B, however, I must be signed in on that console and connected to Xbox Live.
You can still play games on the banned console, of course, but you can't do anything that requires Xbox Live. You can't even download patches. Your saved games will also not work on any other console. They will be labeled as corrupted. You also won't be able to install games to the hard drive.
Basically, whatever happens on a banned Xbox stays on the banned Xbox. If you play through Mass Effect on the banned Xbox and try to migrate your character to Mass Effect 2 on a new Xbox, you will not be able to do this.