If your Ubuntu installation (or any other linux distribution that has a liveCD) is broken and can’t boot because of a faulty update, you can try to update your installation after booting from the LiveCD.
Start a terminal and use these commands (/dev/sda2 might need to be changed to match your configuration, you can use fdisk to figure out which partition is your main one):
sudo mkdir /media/karmic
sudo mount /dev/sda2 /media/karmic
sudo mount -o bind /proc /media/karmic/proc
sudo mount -o bind /dev /media/karmic/dev/
sudo cp /etc/resolv.conf /media/karmic/etc/resolv.conf
sudo chroot /media/karmic apt-get update
sudo chroot /media/karmic apt-get upgrade
sudo chroot /media/karmic apt-get dist-upgrade