Alright. I figured everything out.
For some reason, my "system settings" process was called gnome-control-center. I had never looked into that, actually. But I thought it was bugged. I then removed it...
sudo apt-get remove --purge gnome-control-center
... expecting to then reinstall it and see if it gets better. After the uninstall I tried to access it from the top right system button and guess what... It DID show up with all the configuration buttons!
I have two guesses:
1 - The distro upgrader changed the System Settings program but didn't update the name entry for the menu, because the package was there the whole time;
2 - At some forgotten point I installed gnome packages and screwed up with the Ubuntu's evolution. Then the distro upgrader didn't recognize it or or opted out to leave my choice of using a gnome tool instead of a, maybe, "unity control center"?...
Anyway. There is the info for anyone crossing this issue. I have seen other people in the same situation around the web. I hope this helps someone.
It's the installation of gnome packages and not removing them cleanly.
gnome-control-center is GNOME3 sessions part and not meant to be used in Unity.