No, dont download WordPress, it should be in your Xampp folder.
How did you manage to install WordPress, if you dont remember where it is? Usually its beyond the htdocs folder. Maybe in a subfolder like "wordpress" or "wp", or maybe directly in htdocs, without any subfolder between. You should know that.
and I'm not quite sure how to open my site!
Same as before, enter http://localhost
or similar in your browser. You *really* should know how to call your WordPress, I cannot do that for you, i did not install it on your Computer. Of course you have to start Xampp before calling WordPress. As you copied Xampp onto your new Computer instead of running an installation, you might lack the Xampp Control Icon. You will find the Xampp Control in c:/xampp/xampp-control.exe. Simply create a link on your desktop to that file and then click it.