Your PHP installation appears to be missing the MySQL extension which is required by WordPress.

It turned out PHP5 was not configured to use MySQL by default. This is what I have changed in php.ini compared to php.ini-recommended.

extension_dir = "c:/php5/ext/"
...
extension=php_mysql.dll
extension=php_mysqli.dll
...
session.save_path = "c:/windows/temp/"

Unfortunately it did not help. I was still getting the same error. It was a time to finally read PHP installation manual. And then the mystery was uncovered. In order for PHP to access MySQL, file libmysql.dll from PHP distribution “needs to be available to the Windows systems PATH”. I copied libmysql.dll to C:\WINDOWS\system32 and voilà – it worked!

RTFM!