I copied the new functions.php into the root
First, there is no functions.php in the ‘root’. Remove that file (from root). Files must be placed in their proper locations.
Yes. Three steps. FTP or host file management tool access will be required. Once you can access your site files, I suggest a full backup first.
Each one of these steps are part of troubleshooting.
1. Rename the whole plugins folder to plugins.old
2. Rename all theme folders (not the whole folder) to theme_folder_name.old. Ensure a default unedited theme is in place at this time (upload one).
3. Perform a Manual Update.
4. Rename .htaccess to old.htacccess.
5. Verify that wp-config.php is clean (recreate if needed).
Since we are not positive of the issue, this restores the site to a default setup and should allow access back to site. This also will rule out a server issue (or at least if it is you can report to host that WP is at default).
Test site. Can you login and perform basic wp functions?
Note: ensure you clear your local browser cache.