Recover the profiles onto the new console, or move them via memory stick. When signed into a profile you can download the content from your purchase history on the console by going to the My Xbox Channel, selecting your Avatar's square and then Manage Account.
Then pick Download History and pick what you want to grab again. You can do it via the site by going here
Of course you could move the profile AND content using a memory stick or the transfer cable.
contact customer support....tell them you want to move all your licenses to your new console, they can do this themselves once you have it registered....download them and content again. a Transfer cable can move the data from one console to the new one,
but try and repeat it and it will overwright what you have already done, so maybe a bunch of usb keys depending on how much data you want to move across