Instead of reinstalling ubuntu-desktop there is some alternative solutions that may work
1- If it's not a problem related to drivers from your video card, it could be a problem with gnome or gdm:
Open the non-graphical login screen with Ctrl+Alt+F1
sudo apt-get update
sudo apt-get install gnome-shell
sudo apt-get install gnome-tweak-tool gnome-terminal file-roller
sudo service gdm start
If gdm doesn't start, try:
sudo update-rc.d install gdm defaults
and them
sudo service gdm start
If it start, just login normally and shutdown your computer via terminal (probably if you try to shutdown pressing the button it will just return to the login screen you just launched)
sudo shutdown now
Now it should be working as expected
2- The second possibility is when the problem is with the drivers of your video card:
Open the non-graphical login screen with Ctrl+Alt+F1
Try to download your proper drivers, for example, if it's a card from NVIDIA
sudo apt-get install nvidia-current
3 - There is one other option, changing the default gdm
sudo dpkg-reconfigure gdm
Change to gdm instead of lightgdm
If the command doesn't open a option box, try
sudo apt-get install gdm
4 - If nothing work, just install ubuntu-desktop again, as suggested, cause it will probably take less time then looking for a solution
sudo apt-get install --reinstall ubuntu-desktop
or
sudo apt-get install ubuntu-desktop