Wordpress "Error establishing a database connection" on fresh install

I played with this for a couple of hours and hit the wall. Wordpress is giving me “Error establishing a database connection.”

I have a fresh LEMP install with Debian 7. I created a new MySQL user and a new database for Wordpress as listed in one of the tutorials here. I can log into MySQL with the new user credentials so I know the password I wrote down is correct.

I am 100% certain that the wp-config-php database authentication credentials are correct. If I change the user and the password in wp-config.php to the MySQL root user the error does not go away.

When I run this PHP script with my user credentials I can connect to the database:

$db = @mysql_connect(‘localhost’, ‘username’, ‘password’); if (!$db) echo “connection failed”; else echo “connection succeeded”;

I have even remade the wp-config.php from the “sample” file just to make sure something critical wasn’t damaged elsewhere. I tried replacing “localhost” with my droplet IP address (don’t have a domain name yet).

So I know that my username and password are good. File permissions for wp-config.php couldn’t possibly be a problem? I mean, the PHP file is running and reporting an error.

Could it be that the database is corrupt although this little PHP connection tester is working? Do I need to put something specific in place of “localhost” for Wordpress to work?