This just occurred to me: "Hmmm we're having trouble finding that site," which doesn't sound like WP breakage per se (the other stuff you mentioned does) -- any chance the domain expired, or is pointing to the wrong ip address? Did you try talking to your hosting provider help folks?

The domain has since expired, but at the time (last fall) it had not. And when we tried recently with a fresh install, it was on a sub-domain on my husband's site, so that wasn't the issue either.

Then it's very likely the hard-coded paths in the database are still pointing to the expired domain, so it can't find it. If you try to swap in the new domain by search and replace in the db .sql file, and then import it over the old db using phpMyAdmin, you might be able to get it up and running. You will also might need to take a look at the .htaccess file. It might be ok, unless it's got the old domain in it.