You should probably change directory to some place other than XAMPP's home (!), by putting a command like this in the shell:
cd c:\Users\<your user name here>\Desktop
This* is the command you'll need to back up that database.
mysqldump -u root -B --add-drop-database databaseName > databaseFile.sql
On Unix systems, capitalization matters, so I try to be consistent in case my web site is ever put onto Unix. Be sure that "databaseName" has the same case as you used inside MySQL. I added the "quotes" here because Unix required them -- DOS did not.
mysql -u root < databaseFile.sql
To do this, back up on the old computer and restore on the other (below).
*mysqldump -u root -B --add-drop-database databaseName > databaseFile.sql:
-B --add-drop-database means "add code to create the database if it doesn't already exist, and delete it and recreate it if it doesn't." Or more succinctly: "Don't argue with me about whether the database is already there; handle it!"