I agree, this is a hardware problem. In fact, I reinstalled a clean OS and it started acting this way shortly after the install. This is a problem that plagues many Sony laptop users, apparently.
Apparently, there is a problem with the design of the touchpad, in that it shorts on the aluminum palmrest because Sony decided not to put any insulation there between the aluminum and the touchpad circuitry. So, if your hand is heavy enough when it rests on the palmrest, it will cause the aluminum to touch the circuitry and make the touchpad seemingly go berserk.
Well, you can try this:http://doube.org/sztp.html
Or, if you have long fingernails (like me), you can hook them under the palmrest (between the touchpad buttons and the palmrest) and pull it up a bit.
Sony is just being irresponsible.