I also had the problem, thanks to all this info I’ve fixed it.
I’d just like to add this – (on win-xp with php5) I have php installed at c:\php, the php.ini is there, and all the .dll files are there – be sure to copy php_mysql.dll from phpext folder to where ever php actually uses .dll files (for me it’s c:\php). On your dev box (that you have access to) you can change the location of where php finds the ini and dll files (I think it’s in the apache/httpd config file).
I now have both mysql and mysqli installed, and only had to change php.ini and copy the .dll file to make it work. The WordPress install (and error message) *should* mention that WordPress doesn’t work with mysqli. As someone mentioned above you can create a php script and show all php modules installed with phpinfo() and see that both mysql modules are installed.