Currently Being ModeratedMay 6, 2013 11:40 AM (in response to johnandsteph)
You are allowed a total of 5 computers at a time to be authorized to play content. It is not necessary to deauthorize an old computer if you are attempting to add a new one unless you have reached your five total allotment. From the Store menu, choose Authorize This Computer and enter your Apple ID and password. At that point you should be able to access your previous purchases. I have included two links listed below. The first one goes over authorization and deauthorization. The second article covers how to download past purchases.
If you are still unable to successfully authorize a computer, you may need to reach out to us via Contact Apple Support.
Hope this helps,