After filling in your legacy avatar name on the screen coolnet560 gave the link for, you're taken to another screen where there are two further fields to complete.
One is for the answer to your secret question. The other is for a current email address to which a new password will be sent.
Here's the rubric:
Please answer the 'secret question' associated with your old avatar, OR provide the old email address assigned to that avatar.
So if you never set a secret question for your old avie, there's still a possibility of resetting the password -- IF you can remember the old email address.
It's not altogether clear, by the way, where you should type in the old email address -- I assume in the box for the Secret Answer?
What happens after this, I do not know -- other than being locked out for trying too many times to recall the old email address. (It gets reset after a few hours so you can try again then.)