My ASUS laptop touchpad suddenly stops working – am I hitting a series of keys that is making this happen?
Yes, it is very likely you are hitting a combination of keys to disable the trackpad (nearly all laptops have this option, except for Apple ones it seems).
For Asus, based on a quick Google search, you should press the function key "Fn" + F9. Basically, look for the icon that looks like a trackpad.
If you could tells us what laptop it is, we may be able to narrow it down further but one would presume as a manufacturer they keep this sort of thing pretty standard across the range.