I was stupid, I kept ignoring the warnings that my harddrive space was running low and left a download running in the background. When I logged out, I wasn't taken back to the login screen (LightDM), and when I rebooted I didn't get the login screen either. Instead I got a terminal-like screen that listed drivers/daemons being loaded, but didn't have a prompt. I could still access the terminal with Ctrl-Alt-F1
(and F2
etc).
After barking up many wrong trees I solved it by deleting a file or two. My question is, why did this happen?