You probably haven't installed and/or enabled the PHP MySQL extension. You can check by creating a phpinfo() page and searching for 'mysql'. If it's not there, you need to install and enable it. You don't say what server you're using, but if it's Ubuntu or a similar Debian-based variant, you can do this:
$ sudo apt-get install php5-mysql
$ sudo /etc/init.d/apache2 restart
If you're on another platform, the steps will be a bit different, but you get the idea.