Error establishing a database connection

I am manually downloading WP for my site. I set up a MySQL database with username and password. I edited the wp-config sample file with the updated information and renamed it wp-config. I then transferred all of the files to my root folder. At this point, I’m ready to install, so I went to http://mysite.com/wp-admin/install.php and keep getting the following error message:

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 have checked my username and password and both are correct. The hostname is correct. How do you make sure the database server is running?

Any assistance is greatly appreciated.