One of the first things the login page does is to try to connect to the database. That error is telling you that it was unable to, and so the page immediately fails.
If your username and password are correct, then the only other thing it can be is in your database connection your mysql server is not set correctly.
If the mysql server is on the same server as your site, then this will usually be 'localhost', otherwise it is the domain of the mysql server.
Who is your hosting provider?