judging by the error, the problem is the hostname setting on line 5
$hostname_PowerStoreConnection = "[Name of the MySQL Host Here]";
if you log into your site Cpanel, you should be able to access your database using PHPMyAdmin. In the PHPMyAdmin window, along the top left, it will show the name of the MySQL Host, this is the name you should use in the connection file.
if you nee further assistance getting this information, you should contact your host.