In Short: Name the databases to be restored
Long form explanation -
MySQL is never ONE database, There are always 'information_schema' and 'mysql' - all the rest are created by user SQL processes -- this is your user-defined data. (Joomla, your custom data, WordPress or whatever) In your case, there is also likely a 'phpmyadmin'. On a new installtion or a re-install, you should only be restoring the databases that contain user-defined data.
With a CLEAN XAMPP install - configure XAMPP & MySQL until you have phpMyAdmin working. Next, configure your admin/root account and any users you created plus their passwords as they were on your OLD server. You may have some pernissions thingies to fix (GRANT statements). NOW - restore the user-defined databases.
Although there may be other ways to go about things, this lets YOU know what is happening, and if a step goes amiss - YOU know what was last done.
You'll want to look at your old config.inc.php wihch contains your old phpMyAdmin settings.
HINT: you can read through your backup, its just a huge script of SQL statements to be executed.