Good news: The problem is solved! It was a matter of a lot of narrowing down and playing with database backups.
First of all, I remembered that I had another Revo installation on this same shared server. I don't know why it didn't occur to me to login there earlier, but I logged into that manager, and there were no issues there. So that led me to believe that it wasn't the host's fault, but something on my end, either in my database or files.
The next step was to figure out whether it was something in my database that was causing the problem, or something in the file system. I asked my web host to restore the database from a backup of when it was working fine. They did that, and the manager worked. So that told me the problem was in the database somewhere.
I used DiffMerge to look at dumps of both versions of the databases, but there was too much there to figure out. So I decided to try individual tables. I replaced the modx_system_settings table in the working version with that from the non-working version, and that broke the manager! So then I knew the problem was in that table, and I did a DiffMerge on that.
Turns out that last week when I was fiddling around with URLs in MODX, I had created a system setting for base_url. I don't think it accomplished anything, but I just left it there for some reason. When I removed that setting, voila, the manager is cured.
I guess the moral of the story is backup your database before you start tweaking random settings (I got lucky this time since the webhost had a backup!), and keep track of what you change, so you know what you might have done that would cause a problem. And remember that user error is always a possibility
Thanks for your help guys. By the way, Bob, although it didn't identify the problem, I did purchase SiteCheck and ran it on this site. I think will be a good investment since I work with several MODX sites. It also found some issues with this one that I wasn't aware of.