The weird part is that I installed a fresh installation of WordPress using Lunar Page’s Softaculous system. The new installation had no problems.
I found a pretty nice forum post that has some things to try. Unfortunately, none of them really worked. I have disabled all of the plugins, and that didn’t seem to make a difference. I also installed all of the plugins into my new instance, and that didn’t break that one. I copied all the wp-includes from the new instance to the old one, and that didn’t fix it either.
I would love to fix it for good through. Please comment if you have any other ideas.