First, I tried starting over. That seems to have worked. I deleted the UT2004 folder. Then I pasted in the backup. The I deleted all executables. Then I extracted the patch into the UT2004 folder. Then I did the ut2004.ini edits. So far, so good.
Previously, I had forgotten to delete all executables. When I realized the mistake, I deleted them and pasted in the new executables. I figured that would be okay, but maybe not. Hopefully, no more crashes.