Heather, it would appear that you may have set a password requirement in your Zip Program. That is the reason you are getting that message. You can test this by trying to open another ZIP file on your computer (not a PAF backup one). If you get the same message there, I would say that is what you have done. If this is not the case, you may have your computer setup as a network computer or you may have two or more users of your computer who have set a password requirement.
You could try uninstalling and reinstalling your ZIP program. But make sure you do that through the CONTROL PANEL|ADD/REMOVE PROGRAMS. This should eliminate the password in your Widows Registry, so that when you reinstall it should not ask for a password.
These are only suppositions from a far, seeing I am not able to see how you have your computer configured.