I used the zip file the first time I tried Firebird and ran into this exact problem. It was also a pain in the butt when trying to upgrade. Using the installer makes it just as easy as using the installer for Mozilla. I believe there was a note in the FAQ or somewhere on the website that you must have Firebird unzipped to a specific directory for the registry patch to work, otherwise it will point to the wrong location. While Firebird does work very well, it is a beta/technology demo product and isn't designed for most end users, hence the mess with getting plugins to work.
goates