Unfortunately, windowed mode did not solve the problem.
It blinks to black, like it's flickering on and off, but really fast (multiple times per second).
Here are two videos a few seconds long showing what I mean about the screen flickering:
http://youtu.be/gVvAbZkLgiM and
http://youtu.be/bcs3o9Gvcas
Windowed mode worked when I switched between resolutions in game! Neat! Well, if you know how to fix it full screen, that'd be great, but if not, don't worry too much because I can play windowed mode no problem.