How long had your parents had the PC for before the problems surfaced?
Under the Sale of Goods Act 1979 your parents have the right to reject the goods and claim a refund or repair - the choice is yours. The PC is not of satisfactory quality.
My advice is take the refund. You will likely get a better PC for the same money now.
Have a look online at Dell. Dell isn't everyone's cup of team I'm sure, but we use them at work and both my privately owned laptop and desktop were purchased from them. I've had no problems with the laptop, and only a failed DVD drive on the desktop (which I replaced easily). You will get a very decent machine for less than �400 and a top drawer one for the �1000 your Dad is entitled to be refunded.
Don't expect an easy time from PC World. All Dixon's stores are notorious for not recognising their obligations under consumer law. So your dad may have to raise a small claims action. If he does, that's when they'll probably give in.
Consult your local Citizens Advice - the kings of consumer law.