It seems that a couple of files in a dir are all that prevents apt-get from restarting every time it is killed with Ctrl-Z or Ctrl-C while it is running. Allowing it to restart is as easy as deleting these files.
The error code when that happens is “could not lock administration file” or something. 😉
sudo rm /var/lib/apt/lists/lock
sudo rm /var/cache/apt/archives/lock