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First of all what you need to do is create a database, then you would create a database user, then you need to associate the user with the database. Your host should have been able to explain that to you instead of telling you they can't give you a password to a database. Does your host supply you with cpanel? Do you have phpmyadmin available to you?
I would think you should just ask how to create a database. It would be easier if you have cpanel as an option to your hosting package. Let us know if you have access to cpanel or phpmyadmin, and we will help you get setup, sounds like your host is clueless.
Hope this helps,
John