do we really have to go out of our way to spell the acronym with a dollar sign? is that really clever? why do people do that? companies make money. they try to make as much money as possible. that's business. that's what companies are supposed to do.

anyway You should not need to repurchase anything. Technically your purchases should work fine when you're logged into Xbox LIVE, since the service has records of the purchases made on that account.

This page will help you get your content unlocked when you're offline:

http://www.xbox.com/en-US/support/systemuse/xbox360/licensemigration/

Note that using this will move the licenses from the old machine to the new one, so it will effectively lock all your purchased content on the old machine, and also that you are only allowed to move a single license once per year (as in, you can't just transfer an Arcade title back and forth between two Xboxes whenever you want to). It's designed for system replacements, not for sharing between multiple consoles.