No password needed. Just go here
http://sales.limewire.com/support/pro_lookup.php and put in the password you used to purchase Pro with and it will take you to your personal download page(you should bookmark it). You can d/load it as many times as you like for 6 months from the date of purchase. After that you'll need to purchase it again.
You could also back it up to a disc with your current cpu and use that to load onto your new one. It's a good idea to make copies of software you've purchased. Just in case something happens and you need to reformat or your hdd bites it or something
.