by Howard Miller.
The database settings in your config.php probably don't match the database you set up.
$CFG->dbhost - if the database is on the same machine then this is 'localhost', otherwise the name/IP of the database machine.
$CFG->dbname - the name you gave when you did 'CREATE DATABASE....'
$CFG->dbuser
$CFG->dbpass - the username and password you gave in the GRANT command. Make particularly sure you got the GRANT command right.
Make sure the database server is running. In particular, the following should work on the command line, using all the data above]
mysql -h dbhost -u dbuser -p dbname
(You should be asked for the password)