My experience:
Running PHP version 4.4.4 in conjunction with MySQL 5.0.22 or there around on a Windows server with IIS resulted in the same error message for me.
What I did was to uppdate the libmysql.dll and add the php4ts.dll. These files can be downloaded from http://www.phpdeveloper.org/news/6143 among other places.
Thus this is not a WordPress failure, but a compatibility issue with PHP and MySQL.
