Error establishing a database connection

Hi I’m really new with wordpress and I keep getting this error,

Error establishing a database connection
This either means that the username and password information in your wp-config.php file is incorrect or we can’t contact the database server at localhost. This could mean your host’s database server is down.

Are you sure you have the correct username and password?
Are you sure that you have typed the correct hostname?
Are you sure that the database server is running?
If you’re unsure what these terms mean you should probably contact your host. If you still need help you can always visit the WordPress Support Forums.

I’ve followed all the steps, created the DB according to my wp_config but no go. I’ve read that you need to place all WP files in the root folder but I didn’t quite like that idea. Simply because I have a couple of other folders that I place on my site to run different webpages and it would look very messy. I also don’t want WP to be my “main” site. At the moment, the WP folder in under root (/root/wordpress/wp-admin/).

Must wordpress be in the root to install? If so, can I move the wp files after installation into another folder?