Are you on a netbook by any chance? My netbook does the same thing with
GNOME, but KDE works fine.

No need to re-install BTW. Just open up the package manager in XFCE and
install ubuntu-desktop. When it is done log out and hit the session button
and choose Ubuntu Desktop Edition instead of XFCE. Login and you should be
using the familiar Ubuntu GNOME interface. You can remove XFCE if you want
now that you have GNOME working. If the shutdown problem persists then you
should search for posted bugs on Launchpad.