Not sure what 'each with it's own cpanel' means, but understand about cache issue. Try using the 'search' box in the Site Administration menu on the front page. Search for 'purge'. That should hit on 'purge all caches' link. Click that link. That should take you to the screen were the 'purge all caches' button resides.
One might have to resort to manually removing caches ... using what ever tool you have access to that will allow browsing of files (and deleting them), navigate to data folder/cache/js/
Remove the contents of the js folder ... not the folder itself.
Consider that it also might be related to caches for themes being used on the site. A theme folder can be found at data folder/cache/. Contained therein, folders that are named for the themes being used. Again, delete the contents of the folders, not the folders themselves.
Logout. Clear your browser cache. Login back in again. Fingers crossed!
Is your site in the maintenance mode? Are you logging on as a Admin level user? Looks like one has moved from a Partner site to a remotely hosted site. Dedicated server or on a shared host?
Is the site running any extra plugins originally provided by Partner ... other than core? Do those still function correctly on the sites that work?
'spirit of sharing', Ken