GDM3 is Gnome Desktop Manager, the part you log into in a graphical login, so that not starting would definitely kill things.
Running out of space is a surprisingly consistent problem that prevents booting. You may want to search the forum for information on deleting logs with journalctl, as log accumulation is a major culprit, though the following command should cut them down:
That command should cut you down to 200M of logs, max. Useful when unable to boot, or just periodically as cleanup. I just ran it myself on a machine that's a relatively new installation (only a month or two) and it deleted almost a gig of logs, which... just too much.
I BELIEVE I'm correct in saying that editing /etc/systemd/journald.conf to uncomment SystemMaxUse and RuntimeMaxUse and setting them to 200M should never use more than 200 MB on logs in an absolute worst case scenario, but I'd feel better if someone with more expertise confirmed that. Also, changing the setting requires a reboot, or reloading the config. Reloading the config can be done with systemctl reload systemd-journald