As others have said, I'm sure people are sick of this topic. I'm starting a new one because the most recent I've seen has solved the database connection, but is now on another issue.
I'm trying to set up a local copy of WordPress on Ubuntu 8.04.
I downloaded WordPress and set up the files per instructions. I have the wordpress directory in /var/www/worpress, with the ownership as www-data:www-data. Permissions look OK too.
I set up the MySQL database per instructions, with database called wordpress-private and user wordpress.
When I try to access the install.php file (either from the Ubuntu machine or across the LAN), I see the 'Error establishing a database connection page'.
I'm using phpMyAdmin to administer, and some results look odd to me.
I can access as root, with the password I set up.
The wordpress user can log on to phpMyAdmin, but only if I don't enter a password. If I enter the password I get an error. (I tried commenting out the DB_PASSWORD line in wp-config.php, but it doesn't make a difference.)
So it looks like something with the user/password/privileges. The user has default global privileges - which are USAGE - and all access rights to the wordpress database.
I just tried changing the username/password in wp-config.php to root. This worked. I guess I can limp along for now, but that doesn't seem right.