Your connections file in the 'Connections' folder on your hosting server should look a bit like this:
$hostname_yourconnectionname = "localhost"; // leave this as it is
$database_yourconnectioname = "mydatabase"; // change 'mydatabase'
$username_yourconnectioname = "mydbUsename"; // change 'mydbUsename'
$password_yourconnectioname = "mydbPassword"; // change 'mydbPassword'
$pictuality = mysql_pconnect($hostname_yourconnectioname, $username_yourconnectioname, $password_yourconnectioname) or trigger_error(mysql_error(),E_USER_ERROR);
You will need to check that the username, database name and password are correct for the mySql database that exists on your hosted server. You should be able to check these from your website control panel, or from your hosting provider. These are different from the settings you used to test on a database on your own machine.