Thanks for your help Skrommel.
I know the problem now, even though I'm embarrassed to say I still don't understand how the script works. :p
Anyway, it works if I have a normal screensaver really running. I see the tooltip, cool.
It does not work when I use your MonitorOffSaver.scr, or if the "Turn Off Monitor" timeout setting (of WinXP Power Options Properties > Power scheme) is in effect, or if I am using MonOff.exe.
So ideally, this mouse desensitizing should be in effect when monitor is powered off too.
If it simplifies things, how about combining the mouse desensitizing with MonitorOffSaver.scr and with MonOff.exe?
I personally do not use screensavers for the pretty graphics, I always prefer the monitor go into its lowest power mode, or soft-off.
And there's another potential problem:
The idle timer that WinXP uses to decide whether it is time to start the screensaver / switch off the monitor. This timer would keep getting resetted by the mouse jitters, so that the screensaver would never start. I have one such machine in my work place, it has a off-brand optical mouse. Perhaps the simpler solution is to but a new mouse / mousepad for that machine.