This seems to be a bug with the open source Nvidia driver, nouveau.
The fix is simple but you'll have to use the command line to do it to avoid the screen corruption. To get to a terminal, press Control+Alt+F1 and then log in. If the terminal is corrupted (it might be) let me know and I'll give you a longer solution.
Then follow the second answer here to get
jockey-text to show you the available drivers, then install and enable them.
If the terminal is corrupt or you can't connect to the internet while things are so corrupted...
The simplest intermediate fix (in order to get you into Ubuntu and connected to the internet so you can install the proprietary Nvidia driver) is disabling the nouveau driver at boot. This is a non-persistent fix so if you reboot before installing the proper driver, you'll need to do it again.
- Hold Left Shift as you turn the computer on until a menu appears asking you to select your version of Ubuntu.
- Press E on the top item (assuming it says Ubuntu)
To the end of the linux line (note it may be wrapped), add the word
nomodeset so you end up with something like:
linux /boot/vmlinuz-3.8.0-30-generic root=UUID=... quiet splash nomodeset
Press Control+X to boot.
You should then see Ubuntu in a horrible low-graphics mode but it should work enough for you to get to the graphical Additional Drivers dialogue and install the right Nvidia driver.