Here is a much more straightforward way to connect to your database:
// connect to database server
$dbserver = "localhost";
$username = "username";
$password = "password";
$connect = mysql_connect ("$dbserver", "$username", "$password")
or die ('<br />I cannot connect to the database because: ' . mysql_error());
// select the database
mysql_select_db ("database_name") or die('<br />I could not select database: '.mysql_error());
Localhost is probably the correct value for $dbserver.
As installed, there will only be one account, the 'root' account for MySQL. This should only be used for administration - it is extremely powerful and should not be used by a website to access the database. Set up a more restricted account for your web applications (websites) to use.
From what I can see in Google, there is no root password for MySQL on XAMPP as installed. See the links below. You should ensure that a password is set for this right away.
http://veerasundar.com/blog/2009/01/how-to-change-the-root-password-for-mysql-in-xampp/
http://robsnotebook.com/xampp-remove-default-users-passwords
(By the way, when you're asking for help here, be sure to note what operation system and version you're running on your server.)