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You also have to confirm this, the database might not be on the host webserver (as I experienced with a webhost recently), so using LOCALHOST will not work.
Check with your webhost and ask them for the hostname of their mySQL server.
For example, I was helping someone install their XOOPS and had the same problem you describe. Instead of "LOCALHOST", I discovered the mySQL database is located on mySQL.iserve.co.nz