First off, choose Control Panels off the START (windows logo) menu on the lower left of your computer screen:
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You'll now see the many, many different ways you can customize your Vista/Windows 7 experience. You want "Mouse" settings (why there's no "Mouse / Touchpad" or similar I don't fully understand, just as it's puzzling that there are Tablet options when my laptop isn't a tablet and doesn't support that functionality. That's another story, though). You'll be dropped here:
Not really what you want, but we're getting there. Click on "Dell Touchpad" on the top left and you'll find that this is all just an elaborate path to get to the special Dell trackpad/touchpad control app:
Click on the huge arrow icon and you'll launch a separate application supplied by Dell that lets you gain complete control over the touchpad:
Almost there. Now click on "Touchpad Settings".
There we go. Finally. See where it shows "Taps" "Tap to Click"? Just uncheck that box and click on "Apply" on the lower right and you've disabled the tap to click capability of your Dell trackpad. Close the windows and you're done.
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First of all when I go to Control Panel, there is no "Hardware and Sound" icon as shown in your first screen. However, there is a "Mouse Options" icon which brings up a screen almost identical to your answer screen. However, the availble button are: Button, Pointers, Pointer Options, and Hardware (four in total).