AOL mailbox names missing and unresponsive in Mac Mail

Suddenly in AOL, the 5 favorites don't show their names anymore (Inbox, Sent, etc.) Instead their names are AOL, and when I click on them, nothing happens. (At the very top it says 0 messages, Connection Logging Enabled).

The Mail icon in the dock shows that I have messages but I can’t open them.

I deleted the Mail app from my Internet Accounts and reinstalled it, hoping this would fix the problem. If didn’t . How can I get my mailboxes back?

[Re-Titled by Moderator]

Original Title: Problem with MacMail