Why went dovecot pop3/imap server down?

Dovecot can't find any usable list of users. I may have been at given path (/etc/exim/domains/passwd) or not (configuration may have been inadequately changed). Make sure you know what you are doing using Webmin or managing your server yourself.

A helpful hand of a real Linux/Unix admin might be a best choice.

You can try to start Dovecot in foreground (-F) and see exactly what's happening at startup. Be sure, what do you want it to do beforehand. E. g. is Exim working well?