A rare case for me, but nevertheless... a big thank you to Sylphid, who on the Ubuntu support channel helped me revive my ancient laptop.
As regular readers will know, it's died many times before. Now, I know the cause, the diagnosis, and the cure.
To all of you running Ubuntu, you may want to take note:
Disable Ubuntu X and Ubuntu X (Testing) from Ubuntu Tweak.
Go to a TTY (CLI only, no G/KDM) and completly remove xorg-xserver
sudo apt-get update
then install x/k/ubuntu-desktop, or anything that depends on xorg-xserver, et voila! It works again.
Sylphid, I thank you again.