Thanks for the question. It sounds like you still have access to the username and password of the previous Apple ID, that is great news. You are on the right track, we simply need to authorize your computer to play this content. If you are receiving a message that you have reached the limit of authorized computers, you can authorize previous computers from your account summary page:
To deauthorize all computers associated with your Apple ID
If you need to authorize your new computer and are unable due to already having five authorized computers, you can deauthorize all computers by doing the following:
1. Click iTunes Store on the left side of iTunes.
2. If you're not signed in to the store, click the Account button, then enter your account name and password.
3. Click the Account button again (your Apple ID appears on the button), enter your password, and then click View Account.
4. In the Account Information window, click Deauthorize All.
Note: You may only use this feature once per year. The Deauthorize All button will not appear if you have fewer than two authorized computers. If you need assistance on using this feature, please contact iTunes Store support via email (http://www.apple.com/support/itunes/store/).