To be fair, as someone who repairs computers for a living (including a lot of Acers) I cannot remember the last time I couldn't get the recovery partition to load if the hardware was ok. The shortcut is Alt+F10 when you see the Acer screen on power up, although you may have to repeat this key pressing several times in quick succession.

MrShed is right I believe in the case of the software-related problem. Warranties generally exclude software - although you may have a case if the software problem was present at time of purchase and is not resolved by a 'factory restore'. In terms of hardware, PC World, along with many other resellers, often buy products from manufacturers without warranties to save on costs, and provide the warranty themselves. It is relatively simple for PC World to test things like the RAM and Hard Disk, so it may be worth dropping it into the branch and asking them to test them to rule it out. Of course, there may be a fault elsewhere, but they are quite common parts to develop faults.