I'm not sure what would be causing the problems your having. Generally, using the uninstaller in Joomla will remove your files correctly. It's true our database tables do not remove automatically. That's intentional to make sure user-connections, settings, and all the other data isn't removed when a user uninstalls. Generally, uninstallation is followed by another installation, and having to re-configure or (even worse) make you're users re-authenticate is a no-go.
I'm a bit confused on what you actually did though. Simply removing the files for plugins or modules isn't going to remove a lot of the information that Joomla stores in your database about those files. So the database will think (for instance) the jfbcsystem plugin is still installed yet there's no files there to 'run'. That's bad if that's the case.
Our component installer is smart enough to upgrade the database whenever installed to make sure your database tables are up-to-date with any changes and shouldn't have any problems with re-installing. The message "Component Install: DB function reports no errors" shows that that probably worked properly. However, it may be the installation of our plugins that is causing Joomla issues. Since it still thinks the plugins are installed, it will try to delete the directories first and then copy over the files. If those directories don't exist, Joomla may be throwing an error during the deletion before copy stage.
What I'd recommend is unzipping the component zip package you're trying to install.
* Go to the /admin/install/packages directory.
* You should see about 4 more zip files (the sclogin module, and jfbcauthenticate, jfbccontent, jfbcsystem, jfbcuser plugins).
* Try installing each of those manually and see what happens.
* If you get each of them to install, try the main component zip installer again.
* If any of those separate files fails, let us know if there's a different error message (or anything) we can work with. If not, you may need to unzip each of those file contents into the right folders in your Joomla structure so that Joomla properly sees the files there for the extensions it still thinks are installed.
Hope that all makes sense. Let us know how it goes,
Alex