I bought a secondhand 2001 Fiat Punto from a local small independent car dealer. The car came with a one-month warranty covering mechanical problems. Soon after buying the car, I started having issues where the back windscreen wiper would come on of its own accord and I could not get it to stop, resulting in the engine cutting out. I spoke to the dealer who had a look and could not find anything wrong, and stated that it didn't come under the warranty. Subsequently, the issue has got worse and after taking it to my own garage they carried out a diagnostic test which indicates there is an issue with the onboard computer. Additionally, my garage detected that the transmission bearings were very noisy and need replacing.

I have tried to call the dealer, but the person who deals with these problems was on holiday therefore I sent a recorded letter about the matter. I have further tried to call the dealer this week, but they are not returning my calls. I would just like to know where I stand legally with both issues and whether the onus is on them to rectify both problems?