That's easy, in principle. The pics aren't in Picasa. They are just on your hard drive. So copy them to the new PC (like all your other data, like documents and music and movies and favorites) and bring them in into Picasa just like you did on this PC.
There might even be smarter ways such as exporting and importing the library, but that means that you would have to copy the pics to exactly the same location on your new PC as they are on your old one.
http://picasa.google.com/support/bin/topic.py?hl=en&topic=14609 is the help for the program.
buying new desktop. Best way to get my pics out of Picasa and into what?