Double check your actual DB_PASSWORD and password settings for it. According to the error, you are denied and not providing it with a password.
Another thing to watch for is localhost versus % username settings. These are two separate users, so user@localhost isn't the same as user@domain.
As of PHP 5.5, the MySQL library has been officially deprecated. It is recommended to move to either MySQLi or PDO libraries for your mysql connectivity. See here for help choosing which interface you prefer: http://php.net/manual/en/mysqlinfo.api.choosing.php