Apple TV does not play purchased content after "deauthorize all"

If you Deauthorize All in your iTunes Store account, purchased content may no longer play on Apple TV.

To correct this, deauthorize and then re-authorize the computer that you sync Apple TV with.

1. In iTunes, choose Store > Deauthorize Computer.
2. Then choose Store > Authorize Computer. Enter your account login and password if prompted.
3. Select your Apple TV in the Source list and choose File > Sync Apple TV.