Error establishing database connection in WordPress

This error message is clear that your website is unable to connect to the database.

Usually this occurs when a user has entered or modified their database credentials (database host, database username, and database password) incorrectly. Sometimes your database server could be unresponsive, or your database may have corrupted.

Checking the WP-Config file

<?php
define('DB_NAME', 'database-name');
define('DB_USER', 'database-username');
define('DB_PASSWORD', 'database-password');
define('DB_HOST', 'localhost');
?>

http://www.wpbeginner.com/wp-tutorials/how-to-fix-the-error-establishing-a-database-connection-in-wordpress/