MySQL makes a difference between "localhost" and "127.0.0.1".
It might be possible that 'root'@'localhost' is not allowed because there is an entry in the user table that will only allow root login from 127.0.0.1.
This could also explain why some application on your server can connect to the database and some not because there are different ways of connecting to the database. And you currently do not allow it through "localhost".