Solution 1:

Check your php.ini and make sure that you have the following line un commented:

extension=php_mysql.dll

Solution 2:

You can use the following library if you do not have mysql_connect enabled but have PDO enabled:

https://github.com/AzizSaleh/mysql

Create a new file: wp-content/db.php and place this code in it (update your path to mysql with path to your extracted folder):

<?php
$pathToMySQL = 'C:\\xampp\\htdocs\\mysql\\';
require_once($pathToMySQL . 'MySQL_Definitions.php');
require_once($pathToMySQL . 'MySQL.php');
require_once($pathToMySQL . 'MySQL_Functions.php');

Solution 3:

apt-get install php5-mysql