MySQL is definitely running and your test confirmed that. I edited the my.cnf but when I tried to restart I got this -
$ /etc/init.d/mysqld restart
-bash: /etc/init.d/mysqld: No such file or directory
Your dovecot suggestion returned this -
drwxr-xr-x 3 root root 120 2006-08-16 16:14 /var/run/dovecot
EDIT: Big news - I'm retarded. The user I created in place of root still exists and works, I just had the wrong goddamn password. Anyway, I can get into MySQL now and use your 'select * from users' but it returns a very long, nearly illegible string of information. In the meantime I'll try to read more documentation about this.
2ND EDIT: Getting closer, I hope! I had read a stored password for user 'debian-sys-maint' in a file somewhere and so I decided to try and (re)establish that password in mysql. I entered this command:
mysql>GRANT USAGE ON *.* TO 'debian-sys-maint'@'%' IDENTIFIED BY 'supersecretpassword';
That seems to have solved my startup errors, because I rebooted (only way I know how to restart mysql) and the errors were gone! Let's hope the dovecot situation falls into place as easily.