Change IP to URL on WordPress Multisite

Hi, I’ve created a new WP multisite on an EC2 instance and I’m about to change my development elastic IP to the correct live URL. I’ve read lots of info from the Codex and several posts, but before I go ahead I need to clarify a couple of things that aren’t obvious to me as a novice.

I followed this guide: http://codex.wordpress.org/Moving_WordPress#Moving_WordPress_Multisite

but there are some step not clear to me.
If I edit the wp-config and change my IP with the URL like this: define('DOMAIN_CURRENT_SITE', 'mysite.com'); then I cannot enter inside my database, it gives me “error establish a database connection”.

Just because I don’t want make a disaster, is there anyone able to explain step by step how to do this?

Thanks in advance