Update Failure
If there was an update that made your system non-bootable and they have fixed it in the repositories, you can use the Live CD to run apt-get to get the new files to fix your system.
- Boot the Ubuntu Live CD.
Press Ctrl-Alt-F1
sudo mount /dev/sda1 /mnt
sudo mount --bind /dev /mnt/dev
sudo mount --bind /proc /mnt/proc
sudo mount --bind /sys /mnt/sys
sudo chroot /mnt
apt update
apt upgrade
If you have trouble accessing your network after chroot, you probably use DHCP and can work around this by adding OpenDNS name servers to your /etc/resolv.conf after you use chroot:
nameserver 208.67.222.222 nameserver 208.67.220.220