Sorry, I should have been more specific, you need to be on the Library screen of ADE for ctrl-shift-D.
That will give you a prompt to confirm you do want to delete your old authorization (you do).
This is on your new computer; it is that one that isn't letting you authorize for some reason.
It would actually have been good to have done it on the old one as well.
You will eventually run out of authorizations (6 devices), and then you will need to get Adobe to reset things.
Deauthorizing the old computer would have put off that day; but failing to deauthorize won't cause any other issues.
Often people can't as the old computer is either dead or given away.