I did what I should have done before posting and that is searching. I did, but mentally glanced over what I should have looked at more carefully.
I got it working again. It seems that the two Login\ Data* files got corrupted when being copied over from the older server. As pointed out in a really old posting, the two files needed to be deleted. I was then able to import the CSV file, kinda. After the import, the listing was still empty. Seems that the browser doesn't update the list after import (a bug?). When I manually entered a password, the imported list now showed up. I had to delete the duplicate password.
No idea how the copy got corrupted.