The Problem

It seems there are a number of NVIDIA Graphics Cards that do not place nicely with the Open Source Nouveau driver, some of which is described here.

Installing Ubuntu

If you are struggling to install Ubuntu you can edit the Grub launcher options to get it working for the current session.

With the option you want selected (eg Install Ubuntu) press E

Add nouveau.modeset=0 to the end of the statement that beings with linux.

Then press F10 to resume the boot sequence.

This can also be done once Ubuntu is installed if you are struggling to get to Ubuntu to install the correct packages.

Fixing Ubuntu

To fix Ubuntu properly you need to install the official NVIDIA Drivers either using Software & Updates by going to the Additional Drivers tab.

Or by removing anything that did exist and installing from the ppa. To do this you need to get to a terminal, either over SSH or by accessing another TTY (eg Ctrl + Alt + F1). If neither of these options work use the steps above to add nouveau.nomodeset=0 on boot.

apt-get purge nvidia-* libcuda-* 
apt-get purge xserver-xorg-video-nouveau

add-apt-repository ppa:xorg-edgers/ppa 
apt-get update
apt-get install nvidia-367 nvidia-settings nvidia-modprobe

Afterwards, reboot and there should be no need to edit Grub on start.