The mysqli error was: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2).
I got this error when setting up a new Drupal 6 : The mysqli error was: Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2).
I got it because I had the wrong host, I had "localhost" instead of the real mysql server address.