did you set up your mysql user and mysql database right?

such as
host:localhost (if your mysql and webserver sitting in same machine)
user: phpbb_user (your mysql user name)
database: phpbb_database (your mysql database name ...)

and php_user should have the privielege over phpbb_database.

I have the control to create the mysql database and user. I prefer to create a specific user and database just for phpBB use. (If phpBB has some security hole in the future, it won't affect my other database. Just my opinion.)