Make sure you are already connected to the Internet. Then, open a root terminal. You can do so by hitting CTRL-ALT-F1 and logging in with username "root" and your root password.
Now, at the root prompt, enter the following command:
urpmi x11-driver-input-synaptics
Follow the prompts to install this package, choosing "yes" on subsequent prompts. Once this is done, edit the /etc/x11/xorg.conf file and find the line reading Section "InputDevice". Replace everything between this line and the first line after that, reading EndSection with the following so that it now reads:
Section "InputDevice"
Identifier "Mouse1"
Driver "synaptics"
Option "Protocol" "auto-dev"
Option "Device" "/dev/psaux"
EndSection
You'll now have to restart the X server. The easiest way is to go back to the root terminal and enter the command:
service dm restart
What do you know, the touchpad is now working properly!
This fix has been tested and confirmed on two installations of Mandriva Linux 2009 Spring (a.k.a. 2009.1). The first is the i586 Powerpack running on EeePC 900 and the other is x86-64 Free running on a very old MSI-1029 notebook. Both have an Elantech touchpad. The desktop environment used doesn't modify the results, as it was tested on LXDE, Gnome and KDE in both machines before and after the fix. Notably, the touchpad did work correctly before the fix in the KDM (login) screen! The reason as to why this happened seriously beats me.