If I were doing the work, I would try a new sub-domain to see whether it works, and then if it did, I would next try a manual re-installation of WordPress at one of the existing sites to see whether that might fix things...and then if it did, you would have just done what you have asked about since the only thing different between a re-installation and a new installation is that you already have these three things:
database at the server (site content)
/wp-content/ folder (site uploads)
wp-config.php (tells WordPress where to find the above)
To do a re-installation, first make backups of the above "just in case", then delete all WordPress folders and files *other than* those three, then upload new copies of everything you had just deleted and then log in.