As per the Trello help pages:
Verifying your account
We have only two ways to verify that you are the owner of your
account:
- You know the email (or username) and password of your account and can log in at trello.com.
- You own the email address associated with your account and can recover your password at https://trello.com/forgot.
NOTE: If your account was created via Google log-in, you will also be
able to recover your Trello account by logging in via your Google
account.
Because these are the only two methods to verify your account, it is
critically important that you keep your email address up to date. If
you change jobs, graduate from college, etc. and no longer have access
to the original email address you used to access Trello, you may not
be able to recover your account if you forget your password.
You don't use that email anymore
You may no longer have access to the email address associated with
your account. This happens sometimes when you change jobs and aren't
using your work email anymore. This can also happen if you delete your
email account.
For security reasons, we are not able to change the email address on
your account (see below). Your best bet is to contact your former
employer directly and ask if they can help you reclaim your Trello
account by temporarily re-opening your old email account.
Why can't you change my email address?
For security reasons, we cannot change the email address associated
with your account. If we were allowed to change your email address,
this would expose your account to "social hacking." Social hacking is
when someone pretending to be you sends us an email asking us to
change the email address associated with your account, thus giving the
hacker control your account.
For example, let's say your name is Robert Jones and your work email
is [email protected]. Someone could great a fake email address,
e.g. [email protected], and email us, pretending to be you. They
might say how they changed jobs and no longer use
[email protected] and could we please change the email for
them. We cannot.
Having said that if you have a handful of email addresses that it could be, then use the password reset form for each email. It will email you a reset link (providing that you did actually use one of those addresses)
If you no longer have access to the email address (or don't know what it is) then you are stuck I am afraid.