What authentication were you using before other admin made changes?
Might be able to get to config by going directly to:
https://site/admin/settings.php?section=manageauths
you will be prompted to login using above.
Got ssh access to server?
cd /path/to/moodlecode/admin/cli/
php cfg.php |grep auth
shows the active authentication methods.
If yours is missing one can re-activate it (assuming other config details still remain in DB) via config.php by making an entry:
$CFG->auth='manual,email,oauth2,webservice'
Above is example.
php cfg.php |grep login
might show info that could also be changed via config.php
Kinda hard to guess without a little more info.
Might have to do as Colin suggest! :\
'SoS', Ken