what it is you're complaining about here. There's nothing to stop the company from charging your card before goods are despatched - in fact I would certainly do it if I was in their shoes. Why should an online business send goods to a total stranger unless the money has changed hands?
The company has certainly been inefficient in not responding to your email, but that's about it isn't it? It's entirely possible that the goods have already been despatched - it has only been four working days since you placed the order after all. Your card company will want to know why you're asking for a refund I imagine, and in view of the short time between order date and today they may well feel that you haven't given PC World sufficient time to fulfil the order.
I have no idea what they'll say, and I hope this works out to your satisfaction, but if I was in your shoes I would certainly be waiting a little longer, and I can't imagine anyone else deciding not to use PC World online on the basis of what you've said here.