As well as your rights referred to in my link above, it's worth noting that Section 75 of the Road Traffic Act 1988 makes it an offence to "sell, supply or offer to sell or supply, or expose for sale an unroadworthy vehicle". (That applies both to dealers and private sales).
A vehicle with a broken coil is unlikely to be regarded as 'roadworthy'. (It certainly wouldn't pass an MOT test!). Any responsible dealer should have fixed any such problem before offering a car for sale. (Of course it's possible that the coil broke after you purchased the car but you'd usually hear a ruddy big bang when it did!)