To fix this issue, you need to deauthorize all computers at once through your Apple ID account settings and then re-authorize your new computer. Apple limits your account to 5 authorized computers. If you hit this limit, iTunes locks you out from syncing or playing music on new devices.
Follow these steps to clear the block.
Step 1: Deauthorize all computers
Since individual deauthorization got stuck, resetting the entire list is the best solution. Note: You can only use this "Deauthorize All" option once per year.
- Open iTunes (or the Apple Music app on Windows 11 / Mac).
- Click Account in the menu bar at the top of the screen.
- Click View My Account... and sign in with your Apple ID password.
- Scroll down to the Apple ID Summary section.
- Look for Computer Authorizations.
- Click the Deauthorize All button on the right.
After this you can authorize your device anew