(This is a PSA to make it easier for me to find this information later, and hopefully help others.)
If you're running Crouton on a ChromeOS device, particularly a Pixel, you might run into trouble with version 32, which is currently in beta.
When you log into your chroot, the screen will be black, but the cursor will appear and be responsive. If you're lucky, you might even notice the cursor change in some areas of the screen. If you flip back to ChromeOS and then back to your chroot, the screen will have updated, but will still be unresponsive.
This is a bug with ChromeOS’s updated handling of some hardware acceleration. There is a temporary fix that you can activate by turning off a feature before logging in. Just run the following command in your shell:
echo 0 | sudo tee /sys/kernel/debug/dri/0/i915_fbc
This needs to be redone every time you reboot the machine, as the flag resets.