Is there a user account entry in the DB for root@localhost? In MySQL you can set different user account permissions by host. There could be several different accounts with the same name combined with the host they are connecting from. The most common are root@127.0.0.1 and root@localhost. These can have different passwords and permissions. Make sure root@localhost exist and has the settings you expect.
I am willing to bet, based on your explanation, that this is the problem. Connecting from another PC uses a different account than root@localhost and the command line I think connects using root@127.0.0.1.
