I got the latest installer and the registration window still wasn't appearing on launch after a complete uninstall and then a reinstall on 10.6.8.
So what I did was install Mountain Lion on a separate HD, then installed Logic and Z3ta. The registration window popped up. I pasted my registration code. Then I found out that the registration code inputs into the "com.cakewalk.z3ta+2.0.xxxxxxxxxx.plist" file as the value "ProductKey".
Now you don't have to go through all of that since I just did it for you... what you have to do is create a value called "ProductKey" inside that plist file, then input your registration code into that value, then save the plist file.
Remember, that you will probably have to close and then relaunch your host after you do this if it's open for it to take effect.
I think that the best fix might be for Cakewalk to update their installer to allow you to input the registration code at the time of install with the serial number.