There was no need to remove the original apps before installing the upgrade. The upgrade installer runs the same as the retail installer, it just requires a serial number for a previous version of FCS. Also, just dragging the apps to the trash doesn't fully uninstall studio, there are many supporting files, frameworks, and codecs that are still left behind. So only removing some of the files can mess up the installer, as you are experiencing.
Take the advise posted above and see if that works, if that fails, run a Google search for an app called App Zapper and use that to remove Final Cut Pro, then try rerunning the installer.