Contact your local Trading Standards office for their advice. Regardless of the length of the warranty, goods are expected to last a reasonable length of time before developing a fault.
What is reasonable depends on many factors, including the type of goods ( e.g. fashion shoes vs. workboots), an contributory factors such as evidence of lack of care on behalf of the consumer.
Trading Standards will be able to advise on similar judgements or precedents for a 14 month old laptop. You then have to consider the cost and hassle of taking a very large company like Dell to court.
You may also want to consider a 3rd-party laptop repair centre - I'm sure their prices will be more reasonable. Try click here= for a range of options.
I claim no legal or consumer rights expertise, but there are several highly knowledgeable members of this Forum who are undoubtedly capable of giving more detailed advice. If there are no knowledgeable answers given by tomorrow afternoon, I suggest you refresh this thread to send it back to the top of the page.
Simply type 'refresh' into the comments box at the bottom of the screen and click the 'Submit' button.