did Comet do it, or did they advise you to contact Sony yourself?
Under current consumer legislation any fault which manifests itself within six months of the day of purchase is deemed to have existed on the day of purchase, unless the retailer can prove otherwise. This means that Comet must either repair the machine within a reasonable time frame, or provide you with a new machine.
problems can creep in once you take on any responsibility for dealing directly with the manufacturer. Any work that Sony do is carried out under the terms of their warranty, and is an entirely separate matter from your contract with Comet.
I suggest that you tell Comet you want a fully-functioning computer. Say that the repair carried out by Sony has not been successful - the machine has failed again, three days after its return. tell them that you are rejecting this computer as not conforming to contract under the terms of the Sale of Goods act 1979, and that you want a replacement. Be prepared to meet with resistance - Comet will almost certainly want Sony to take the computer back yet again. You'll have to play this as you go along, but make it quite clear that you are rejecting the machine - use the word.
The law doesn't define what is a reasonable time for the rejection of goods, but the shorter the interval between purchase or rejection the better. That's why I mentioned resistance - Comet may well take the view that three and a half months is too long. You'll need to be firm but polite - diplomacy usually works better than aggression in these circumstances.
Let us know how you get on.