If phpMyAdmin works, MySQL itself is probably working right.
I would open up MyAdmin, and use the browse feature to make sure you have the database name correct (there are rules, and you may have broken one) Then use the Privileges tab to see who has rights to that database.
How far did you get in the WordPress installation, or are you doing a mover? In order to get it working, try installing clean rather than transferring and backing up. There are tricks in the WordPress backup & restore process, like URL's that may need to be edited in the database (JonB know from things not working right). If a clean install works, then you know your problem is with fixes in the wp-admin, or MySQL etc.
If you have done a move, this page has bee useful to me:http://codex.wordpress.org/Moving_WordP ... New_Server