However, when a retailer chooses to attempt a repair (rather than to offer a replacement), they have a duty to minimise any inconvenience to the customer and, in certain circumstances, to pay compensation to the customer for the inconvenience or costs incurred. (For example, your nephew might have the right to claim compensation from PC World for his repeated travel costs to and from their store). With repeated repairs, there obviously comes a point when the inconvenience to the customer (through the repeated temporary loss of his computer) becomes 'unreasonable'. There is no statutory definition as to when this point is reached but many firms, including PC World, work on the basis that the inconvenience to the customer becomes 'unreasonable' after three attempts at a repair. At this point they then have to offer a replacement item.
If your nephew wants to try to get a replacement for his laptop, he must argue on the basis that, irrespective of the number of repair attempts already carried out, the inconvenience to him has now become unreasonable and that, because of this, PC World have now forfeitted their right to offer a repair. If such forfeiture can be established, PC World must now offer a replacement.
Chris
PS: Your question refers to the fact that the laptop is still under warranty. I advise that your nephew should make no reference to this when trying to get a satisfactory response from PC World. A warranty is a 'gift' from a manufacturer and is unrelated to the statutory duties of the retailer. Most retailers will leap at the suggestion that the purchaser intends to claim under the manufacturer's warranty; this effectively allows them to 'pass the buck'. Forget about the warranty. Stick with arguments based upon your statutory rights to receive a suitable remedy (with minimal inconvenience) from the retailer.