I suspected that the problem had to do with the upgrade that I installed, and I was right. Looking through the Kubuntu Guide for an answer, I found this:

Sometimes after a kernel upgrade a proprietary driver may stop working. In such a case, try installing the new linux-headers that match the newly upgraded kernel:
sudo apt-get install linux-headers-$(uname -r)

Logging in to the command line, running the above command, and rebooting solved my problem and brought back the GUI. If you run Kubuntu, Ubuntu, Debian, or a similar GNU/Linux distribution, try executing the above if you find yourself staring at a black screen with a text welcome instead of the familiar graphical login screen that you’re used to.