I am using PHP and MySQL to make a database connection, the only change is that I am trying to access my remote server from my local computer using my server IP address.
Most default installs of MySQL only listen to the local machine.
Look for the bind-address setting in my.cnf on the server, and make sure it's listening on the IP address you're targetting. You may also need to ensure skip-networking isn't switched on!
Alternatively (and less securely!) the following will set it up to listen on all addresses - local and remote:
bind-address = 0.0.0.0