Well, after some diagnostic help from Dave Ifversen last night, Gretchen and I have now repaired the defective power switch mount on Katie's computer with the aid of a hot glue gun. I had to trim some excess glue off in order to get the switch mount back in the proper position, but everything seems to be working correctly now.

It's entirely possible that most of the flaky behavior of the computer can be traced to the flaky power switch. We'll see.