Ok, I just tried making a /var/run/mysqld directory as described here:
http://ubuntuforums.org/archive/index.php/t-551741.html
And this is not the solution. Running "/etc/init.d/mysql start" still does nothing. I also notice that nothing's logging in /var/log/mysql and the /var/log/mysql.[err|log] files are empty.
Anybody have a clue?