Go back to shop and claim under Sale of Goods Act 1979, not unreasonable to expect computer to last more than a year. Their initial answer will be 'no' so you may have to take it further. Remember a warranty is an addition to your rights under SOGA, not a replacement.
You may have to get an independent report from an expert to prove the fault was present when you bought goods and was not caused by your misuse. Information from Samsung would be helpful.
Which Guide to Sale of Goods Act
http://www.which.co.uk/consumer-rights/regulation/sale-of-goods-act
Problem unlikely to be motherboard. There's a known problem with the UEFI which is the internal program the laptop uses to start itself up before loading Windows. In short, it's a Samsung programming error. Search for 'bricked samsung laptop'.