not sure if this qualifies as an answer, but if you haven’t already, you’ll probably want to ensure that port 3306 is open on mysql server ip address. From the webserver with the php pages, you’ll want to issue:

telnet <mysql ip address> 3306

just to make sure there is connectivity. You may wish to install the mysql client on the webserver installation as well, just to check if you are able to login properly. If you are using ubuntu,

apt-get install mysql-client

and then connect with:

mysql -h<mysql public ip> -u<user> -p<password>

Can’t say much about PDO since I’ve never used it, but I had apparently got mysql connectivity some years ago using mysqli. It’s been a while so the information I have below might be incorrect:

(http://php.net/manual/en/mysqli.quickstart.connections.php)

function connect() {
                $con = new mysqli ("<host>","<username>","<password>","<database schema>");
                if (mysqli_connect_errno($con)) {
                        echo "Failed to connect to MySQL: " . mysqli_connect_error();
                }

        return $con;

        }

@9focuspoints

Most shared hosting providers block remote access to anything other than SSH, if they provide SSH access to their customers at all.

The primary reason for blocking port access is security. It’s also the primary reason that any VPS or Dedicated Server should be using a firewall configured to block commonly accessed ports and the Private Network IP should be used in place of the public (where possible).

While the web hosting provider could simply block each IP, throttle connections, etc, when you’re a provider that’s hosting 1,000+ clients on a server (not uncommon for the cheap-o providers offering the world $1 - i.e. every single “unlimited” provider on the market), it’d bog service down even more allowing such and they’d spend more time handling issues in this area than elsewhere.