Thank you for your rapid and helpful response. I eventually removed all the junk left by the one-click people. Now things seem to be working properly.
Here are some things that might help the next person who has this problem.
1. The uninstall function provided by the one-click people did NOT remove the entire install. I found folders and files scattered around my web space.
2. The uninstall did not remove the database created by the install. There are probably good reasons for this, but it meant that some of my available database slots were taken up by unwanted stuff.
3. Once the old junk was deleted and I had removed the excess databases, it was easy to install WordPress manually.
4. Before I did these things, WordPress was unable to connect to the new database I had created, in spite of the fact that I had supplied the correct information.
The moral of the story is: DO IT YOURSELF!
Thank you, bcworkz, for your calm reassurance. Now I’m going to eat a cookie.
