Remotely accessing web server, and connecting to local mysql (via php)

I am trying to connect to my local mysql server via php. so my code looks as follows:

$con = mysql_connect("localhost", "user", "password");

mysql_select_db("database", $con) or die('ERROR 4');

ok, we've all seen that before.

So when I run this PHP script on the machine with the mysql database, everything runs fine. But once I access this script remotely (on the server, with the local mysql database) it cannot connect to the database.

Is there any way to make it so the PHP code connects to the mysql database via a local reference? Or do I need to look into connecting to the mysql database through an IP address?

edit: To clarify, when I access the script on the server from somewhere else, it doesn't work

edit 2: When I check the error log it states "Call to undefined function mysql_connect()"