The Authenticator information was lost after the app was reinstalled, which made it impossible to log in to Trello.
Welcome to the Community!
I am sorry, but if you have completely lost your authentication application, there is no simple fix.
When you installed your authentication application, you will have been given some codes and methods to recover it in case of emergencies (simple example, if you set up the google authentication app on your 'phone, it'll give you a series of codes you can use to re-create it in the cases where your 'phone gets lost, stolen or damaged beyond repair, on a new 'phone)
You should use those to recover your system.
If you can't do that (I do not know how you lost your authenticator information), then you will need to go through the process of proving who you are and that you are the owner of the site. Or, if you were just a user, not the owner of the Trello system, you'll need to talk to your admins about regaining access.
Re-stating the problem does not give us any more information that might help us to help you.
You'll need to recover your authentication data from the recovery systems you created when you set up your authentication method. Or, you will need to establish new authentication routes by contacting the support team for Trello.