If you go to All Photographs in the Catalog Panel of the Library Module and search for one of them by File Name, does Lightroom find it?
Yes, it did find it. And, after several hours or struggle, I finally got everything pointing to where all the parts can find themselves. Far too complicated to explain, but the most helpful was shutting down and disconnecting the external hard drive. Upon reconnecting, everything seemed to remember where it was. Magic.
Thanks for the help.