I have a dell, no disable button like HP there. And what you describe above is what I meant earlier, it doesn't have the disable option in 'hardware'. It's probably because I don't have the latest drivers. But I was too lazy to browse dell's crummy site for them so I just disabled 'tapping', that should get rid of the phantom clicks.

btw, "touchpad (the square used to control the mouse)" <= this was kinda funny.. I'm in my last university year of civil engineer computer science so eh.. I'm kinda familiar with computers..