Setting up CiviCRM in WordPress - warning message and failure to connect to WP DB
I had a GoDaddy Managed WordPress account and the same is happening to me. I've checked all information (db server, username, password, database) and all seem correct. But still the got message 
"Your database settings don't appear to be correct. Please check the Database Details below for specific errors." 

After many calls to GoDaddy support, I gave up and changed to a regular shared hosting account with cPanel. This time the CiviCRM setup worked as expected and everything is working perfectly.

GoDaddy didn't provide a good answer, so my guess is that Managed WordPress hosting doesn't provide the access required by CiviCRM.

Hope this helps in any way.