Just to make sure, go to the root of your SuiteCRM installation and do
ls -al themes/SuiteR/css/style.css
to check is that file even exists on your SuiteCRM installation. Note the group and user ownership of the file, and the permissions.
If the permissions aren’t right, as i believe, set permissions correctly, following the steps on the link I gave above.
I don’t know why the permissions diagnostic says you don’t have a problem with permissions, but you clearly do, since your web server is not able to serve the file. That’s why the screens aren’t showing correctly. It seems the diagnostics are misleading.
You must know under which user and group your web server is running, in order to do the correct chown command.
At least make sure the permissions for that file get corrected and see if you can now load the file from the browser.