OK, I think we're getting somewhere.
First I ran the oldest one: 2.6.38-12 generic (recovery mode)
when prompted I told it to resume a normal boot.
This loaded Ubuntu's login screen (the GUI). I didn't bother experimenting past that point since - as I was warned - the graphics were wonky.
So then after this, I rebooted again and now loaded 3.8.0-19-generic (recovery mode)
Same as before, I told it to resume normal boot.
This time, at the login (in the terminal/CLI) there was an error:
shoaxing login: initctl:event failed
Then it just goes black and does nothing.