This post is not meant to be a how to, but rather a compilation commands that could be helpful in trying to fix issues with the login screen after an upgrade.

These commands should be executed from a prompt, you can get to one using the ctrl+alt+f1 (you can replace f1 with any of the function keys from 1-7), or you can boot up from recovery, or you could mount the drive and chroot into it.

Reinstall Desktop and Login Manager

sudo apt-get install --reinstall lightdm ubuntu-desktop

If your using using Gnome Shell

sudo apt-get install --reinstall gdm3 gnome-shell

Reconfigure lightdm, set it as the default login manager

sudo dpkg-reconfigure lightdm

Replace GDM with LightDM

sudo apt-get remove gdm3 
sudo apt-get install lightdm

Installing GDM (Gnome Login Manager)

sudo apt-get install gdm3

Remove Intel video and Plymouth

sudo apt-get remove xserver-xorg-video-intel plymouth

Reboot, get to a prompt and reinstall login manager, replace lightdm with whatever one your using

sudo apt-get install --reinstall lightdm

Reinstall Intel video and Plymouth

sudo apt-get install xserver-xorg-video-intel plymouth

Install Ubuntu Gnome Desktop

This seems to solve some of the issues with GDM3 not starting up.

sudo apt-get install ubuntu-gnome-desktop