Tough one, but, have a look here: http://www.moneysavingexpert.com/shopping/consumer-rights-refunds-exchange. How strongly do you feel about it? You can play the game on the external monitor. Is that a bind? Do you do lots of other things on the machine and they are fine? So, can you live with that? On the other hand if this is a really big part of what you bought the machine for then it is clearly faulty, their 4 day attempt to fix it is clear evidence, they could not fix it, in fact we know they can't from our research so far. I'd get my argument lined up and not take no for an answer on a swap for something else, but even so, if there is nothing suitable, a refund. Its up to you though, I'm just on a high horse there, you choose.