I have a problem with my WordPress DB after I tried to install multi-site

You most probably only added one of the following in your wp-config.php file thinking they were the same, as m73mitchell and I had done:

define('WP_ALLOW_MULTISITE', true);
define('MULTISITE', true);

I couldn’t find any documentation why they have this counterintuitive setup, but just add the one you missed and it should work.