Well, I may not know enough about Directadmin to help out much on this forum, but I have installed phpBB on a plethora of sites.
Are you sure it properly wrote to config.php? Download it from your server and check if the database login info was saved correctly.
Also, IIRC, you need to delete any install files (install.php as well as the /install and contrib/ directories) before the forum will become active.