Can you go to Device Manager > Mice and other pointing devices. Right-click Synaptics > Properties. Try Rollback Driver or Update Driver or just plain Uninstall it (including driver software)
You may also need to DisableDriversinWindowsUpdate
You could also see if you can find an older version of the driver on HP Support and Download or elsewhere on the web
Do you not have a small button or Function key that is supposed to toggle it on / off?
There is also a method of disabling any reinstall or change of any driver to the Touchpad (Setting Hardware ID Restriction)
See how you go.