What package did you download and put on your website? Is it an update package or fresh install?
It may be that you have overwritten your config while which has the dbname,username and password required to access the database. Also as well as updating files you have to run the file in the install folder which will be called /install/update_to_latest.php which updates the db tables.
check that your config.php contains the info you think it should (don't post the information in it for others to see as has been done in the past)
Patience of a Saint :: Memory of a Goldfish.