Q: Computer authorized/not authorized loop

I am having the same problem.

Try If iTunes prompts you to authorize your computer when you try to play iTunes Store purchases - Apple Support.

tt2

Try Reset the Lockdown folder in iTunes - Apple Support.

Are you able to use the iTunes menus to both deauthorize and then authorize the account in question? Even though you can no longer access the old email address the address and password combination should still work if you remember them, unless we are talking about old AOL screenname accounts.

tt2

Ah, in that case you're going to need the assistance of the iTunes Support team. IIRC there was a limited window in which you were supposed to arrange for the migration of the account however I don't recall the exact details, or whether they can do something now that the original migration scheme has closed. Hold on, perhaps the details you need are here: AOL Usernames can no longer be used with the iTunes Store - Apple Support.

tt2

Компания  Эппл вымогает у пользователей деньги на покупку новых гаджетов, так как не решает проблему забытого пароля от ID! Обращайтесь в суд за восстановлением своих прав!

Company Apple users extorts money to buy new gadgets, because it does not solve the problem of forgotten passwords by ID! Contact the court for restoration of their rights!

Apple should be able to help if asked nicely.

tt2

Visit iTunes - Official Apple Support and scroll down to the contact support option at the bottom.

tt2