I am not sure as to which touchpad you have exactly in the HP, but I have seen this behaviour on touchpads emulating twofinger actions which were not really supported.
Check if you have an /etc/X11/xorg.conf (or anywhere else for that matter) and see if these lines are present:
Option "EmulateTwoFingerMinZ" "35"
Option "EmulateTwoFingerMinW" "8"
If so, comment them out by putting a '#' in column 0
Check /var/log/Xorg.0.log to see which xorg.conf is used from where, if any. It is mentioned near the top of the file. Check this log file also for any signs of emulating the twofinger actions.
You might also check this page: http://wiki.debian.org/SynapticsTouchpad