I got asked to look at one my parents PC's a couple days ago as it had 'locked up'. Upon investigation it hadn't locked up but the motherboard had fatally broken with the PS2 and USB ports left lifeless. I was able to SSH into it and the machine was just fine.
I wasn't able to easily get any data off the HD while in the case so popped it out and took it home, plugged it into another of my own PC's and booted it up. GDM failed to come up and I was greeted with the typical "X has failed to start" message and dumped to a prompt. Not a problem, I've been here before and we can fix that in a jiffy.
sudo dpkg-reconfigure xserver-xorg
Go through the various questions, most of which are pretty simple and you can pretty much take the defaults in my experience.
A quick reboot:
sudo shutdown -r now
or a faster restart of gdm (the login manager)
Everything should be fine when it comes back up.