A guarantee is entirely separate to your legal rights. (It's a 'gift' from the manufacturer or retailer, which can be as generous or restrictive as the provider chooses to make it).
Your legal rights are defined by the provisions of the Consumer Rights Act 2015. If something goes wrong within the first 6 months after purchase there's a legal presumption that it must have done so because of something which was wrong at the time of purchase (such as the use of poor quality materials or poor workmanship) unless the retailer can show otherwise. So the retailer would then be obliged to repair or replace the defective item.
Thereafter the law ceases to automatically presume that any fault which develops must have come about through something which was wrong at the time of purchase. It's up to the purchaser to establish that it must be so (e.g. through getting an independent assessment of the item). If he can't do so, then the retailer is under no obligation to repair or replace the defective item, as that obligation only exists when there was a fault present at the time of purchase.
http://www.which.co.uk/consumer-rights/regulation/consumer-rights-act
So, unless you're able to show that the current problem came about through a fault which was present at the time of purchase, your statutory rights won't help you. (I'm assuming that the initial 6 month period has passed, of course).
You might still be able to fall back on the guarantee but, because it's separate to your statutory rights, you'd need to read the exact wording carefully. (Guarantees can be very hard to enforce). For example, if it only says that, in the event of something going wrong, the manufacturer (or retailer) "will make reasonable efforts" to remedy the fault, it could be claimed that they've already done that.
You should also check very carefully to see exactly who offered the guarantee. There would be no point pursuing the retailer if the guarantee came from the manufacturer, or vice versa.
It's also worth asking yourself whether you're prepared to risk the costs of court action if the provider of the guarantee refuses to honour it. A threat of bad publicity can sometimes be far more effective than one of court action, so suggesting that your local newspaper might like to carry the story could possibly get something done for you.