Ever purchased a new Box and wanted your old Xbox Live content on it? I’ve been there once, and had a friend with the same issue.
Microsoft has given us a solution. Their tool can only be used once per 12 months, so you won’t be able to exploit the system. It just helps for when you’ve purchased a new and separate 360 because your former was out of warranty.
From their site:
Got a new Xbox 360Â® console? Great. But maybe you downloaded games or other content from Xbox LIVEÂ® Marketplace onto an older Xbox 360 console, and now you want all that content on your new system. Well, now there’s a way to do it.
With the license transfer tool, you can transfer the licenses of all your previously downloaded content from your old console to the new one…
Note that if you received your new Xbox 360 as the result of a refurbishment or repair, the licenses have already been transferred as part of the repair process, and you do not need to use the license transfer tool, but you may need to download the content again. Check the repair and refurbishment instructions page for more information.
Handy dandy. Check the source link for directions and where to start the process. Good luck!