I installed gnome-shell and attempted to log in to a Gnome session, but there is something wrong with the graphics driver or something; all animations are accompanied by a lot of fuzz, blocks of random pixels are everywhere, so I decided to switch back.
Now the default Ubuntu session doesn't start Unity any more. The only session that works as it is supposed to is Ubuntu 2d. I've already followed the advice on the other questions: Removed gnome-shell, gnome, gnome-fallback and all associated with it, removed and reinstalled ubuntu-desktop, and it did not help. Not sure what is going on here.