I just heard this on Major Nelson's podcast, so some one else may have already posted it up, but there are folks here who NEED this solution, and I'd prefer to err on the side of being too helpful.
So, anyway, for folks who had their 360 replaced by Microsoft, but can no longer play their old DLC on their replacement system off-line or on other accounts, apparently there IS a solution.
1) sign in to live with gamertag that originally purchasedthe content
2) go to marketplace
3) select account management
4) select download history
5) select content, and download again
According to Major Nelson and E, this grants a new lisence to the replacement system, allowing you to use the content offline and on other gamertags, just as though you had bought it on that console originally. I believe you have to download each item individually, but it beats not being able to have any of them at all.
Anyway, I hope that helps some one.
Posts
Let us know how well it works, and I'll edit it in to the OP.