Profile with mail settings and stuff is in C:\Windows.old\Users\\AppData\Roaming\Thunderbird\Profiles\.default\
%AppData% resolves to the Roaming directory, not the Local one. This is even if the email folders have been stored elsewhere.
Useful information about passwords
Thunderbird’s email account settings are all stored in the user’s profile folder. To get the whole setup back, just copy the profile folder from the old machine to the new one.
For me, my email storage location still had the same path, so there was no issue with the actual emails themselves.
For information about moving profile, see https://support.mozillamessaging.com/en-US/kb/profiles