NOTE: I do not have physical or console access to the above server!
The problem you're experiencing is a perfect example why I always make sure I have shell (ssh) access to the server.
Since I'm able to gain direct remote access to your database on your web host but you can't access it through your web site on that server, shows that the database access rights aren't setup correctly. I don't know if that's due to a mistake on your end or your web host, but at this point you should contact your web host.
If you haven't reset the access rights, I might be able to login and fix it for you, but that would not be appropriate.