Here's an update.
At the suggestion of M. Langdon (see above), I removed Moodle version 1.2 and installed version 1.3. Now almost everything works!
I used the same database I had before and didn't even empty the tables. (I also have another application using that database.)
I'm having trouble getting the user pictures to upload, but I can tell that it's something to do with my dataroot setting. I will probably get that figured out.
Perhaps 1.3 should be promoted to an official release? Or, as verison 1.25? Any, it's working well, even on 1and1 hosting.