My problem is fixed, but I can't really mark this thread "Resolved," because I don't know how it was fixed. I spent a couple of hours poring over the WP documentation, and I tried various ways of migrating my database from MySQL 4 to a new MySQL 5 database -- through phpMyAdmin and through SSH, but kept getting errors, mostly server timeouts. My blog is nine years old and contains several hundred posts and lots of comments, but it's not really so big that the server should have choked on it. I also tried going back to the old database, backing it up AGAIN, and trying to import the newer backup, but that didn't work either.
Finally I called my host (1and1 Internet). Of course they had to make me prove that I had done all the preliminary steps (plug in my computer, edit wp-config, back up old, import into new, etc.), but eventually they were convinced that there was something wrong that I couldn't fix on my end, so they manually moved the database themselves, which took about five minutes and fixed everything.
I wish I knew how to do that, but I don't, so... issue repaired, question not really resolved in my mind.
Thanks for your suggestion, Josh!
