Trying to think of some way to re-build the site without losing everything, I wonder if this would work:
1. Create a new empty database.
2. Rename wp-config.php to wp-config0.php.
3. Visit the domain and run the WP install, supplying the new database name to produce a new wp-config.php.
4. Start putting things together again piece by piece.
The advantage would be that all the uploaded stuff (plugins, theme, media) would be there, ready to be used. I don't know if the Media Library would be recognized as being in place.
If, during the rebuild, it was necessary to look at the old posts and pages, a rename of the two wp-config.php's could get you back to the old site.
Have you ever heard of someone doing something like that?