That content is in what is called the profile. if the old computer is windows, and if you didn't customize locations of folders, do this - start old PC and do NOT start thunderbird - copy c:\users\<yourid>\appdata\roaming\thunderbird to external media - on new computer, exit thunderbird if running - copy the thunderbird folder from external media to c:\users\<yourid>\appdata\roaming to overwrite the default profile. - start thunderbird and your old profile, including accounts and folders, should appear.

For future reference, the user is responsible to saving the profile, as thunderbird does not have an online cloud server to do that for users.