Silly me. I have resolved the issue. The config.php file was root:root. I may have copied the file after I changed the permissions for the directory tree. I discovered the discrepancy when I was comparing the directories.
When I changed the permission, the upgrade started under notifications. However, I received a timeout, and when I refreshed the page, I had to log back in. The old version is still listed, and I don't get an update request under notifications.
I was hoping the upgrade to the new version would resolve my timeout issues.
Thank you both for your suggestions.
I closed firefox, and logged back into the Moodle. Now it is upgrading to 2.5.9. There are a couple of add-ons missing from disk (lab, pdfview, communication, grade, news, and research.) I don't know if those are particularly important. The site has no external connections, and all of the students sit in the room where I am now.
I'll do a quick look through the old directory for Add-ons before I click Upgrade Moodle database. Or, would it be easier to upgrade now and add the labs later?