Using Media Temple as my web host, I was getting the following error message: "Critical error: Could not connect to MySQL server!Can't connect to local MySQL server through socket '/var/run/mysqld/mysqld.sock' (2)"

Avram at CubeScripts was nice enough to help me with the following solution:
"Find out which socket Media Temple uses to connect to MySQL server. (Instant Update uses default socket.) In your MySQL server address field (in IU installer), replace 'localhost' with that information. It accepts identical parameters as first argument of PHP's mysql_connect() function. It can also include a port number. e.g. "hostname:port" or a path to a local socket e.g. ":/path/to/socket" for the localhost. You can also find socket address in phpMyAdmin, if your web host provides one."

It was this last point that fixed my issue. In phpMyAdmin your server name is displayed prominently in the upper left near the phpMyAdmin logo; mine began with 'internal-' and ended with 'gridserver.com' I swapped that in in place of 'localhost' and it fixed the issue.