The last updates installed were:
- Package: xserver-common, version 2:1.6.4-2ubuntu4.1
- Package: xserver-xorg-core, version 2:1.6.4-2ubuntu4.1
Either way, I don't know exactly what the problem was, but here is the solution I found. My '.Xauthority' file in my home directory was the problem. I don't know what was wrong with it, but after I cleared that file of all contents, KDM let me log in normally. I hope this fix works for anyone else.