because PC World doesn't 'guarantee' anything. They may well offer a 28 day warranty, but that's a different matter, and can only be in addition to, and not in place of, your rights under current consumer law.
The correct position is that a supplier is liable for faults which manifest themselves within six months of the date of purchase, unless it can demonstrate that the fault was not present at the point of purchase. In practice that's a very difficult thing to do.
Your contract was with the supplier, so it is to the supplier that you look for a remedy. The law says that the remedy is for the supplier to either repair the goods within a reasonable time, or make a full replacement.
You may completely ignore the 28-day condition, for it has no force in law.