Lost your Login Key
There is exactly one way back in: prove you still control the Bitcointalk account this Academy account was verified against. That is the same Personal Text check you did originally.
If you linked a forum account
Start the verification flow with the same forum UID. When it succeeds, we issue a fresh Login Key and retire the old one.
Start recoveryIf you didn't
Then the account cannot be recovered — by you, by us, by anyone. That was the trade for not giving us an email address, and we said so before showing you the key. We are not able to make an exception, because an exception is exactly the hole an attacker would use.
You can start a fresh account. Course progress will not carry over.