[IT WAS: Gnome Shell only works when using external monitor]
I will reply to myself.
It has been loike an Agatha Christie's novel: too much false trails, too many suspects. Finally it was not the external screen, the background picture or the many startup apps fired by gnome-settings.
The real difference was the printer server we use at job (and it's not available at home)!
At job we have all Linux clients with th CUPS server disabled and the following content in /etc/cups/client.conf :
At home it made a timeout and it crashed the gnome-settings daemon and so the whole gnome-session/gnome-shell.
I think this is a bug of GNOME/Fedora: the user session shouldn't crash because there is no printer server!