This scam is almost as old as outsourced call centres in India... I guess you should have bought a Mac instead.

BTW, anyone that did get suckered in to paying them money and letting them remote control their computer better make sure they didn't install a remote trojan that will give them access at a later point. I have recently heard of a variation of this scam where they will call back a few weeks later and surprise surprise there is now something else wrong... apparently they remotely installed some nagware without the users knowledge that now gets removed, you guessed it, for a price.
Apparently this started around June 2010 and police is pretty much powerless because the scam originates from outside Australia plus they are not really doing anything illegal. Morally wrong yes but apparently it's not illegal.
I guess the best way to deal with them is like what this guy did: