Two hours of my life are gone but here is what I did to fix. First, I deleted the Category Base entry and ignored Structure. It updated fine but the site was still MIA. Whenever I went in to Permalinks admin, ht was immediately corrupted, so I was just going in circles. This last time, I went in to Perm Admin, then deleted the ht file, then deleted Perm instructions, and it updated properly.
My baby has come back.
Thanks for your help.