Godaddy's databases are named: something.godaddyservername.com
I had a few mainstream sites there a number of years ago, and I vaguely remember them not using 'localhost' but instead all MySQL databases are run vie their own system and name calling.
But if you do not want to trouble yourself with shit like this, get yourself a real host, save some money and get help when needed. Host with the best,
host with Amerinoc right here. They will even move your existing site for you, so you can be up and running with them, trouble free in a few hours.