Sold me a faulty car

Bought a car in September and they assured me it was service and went through a roadworthy test. Oct 3 which was hardly a month the car showed warning signs for battery system and water. Messaged the salesman Joe and he simply told me to go to the garage and fill the water. On 1 Jan the car gave in as the alternator was finished. AVW specialist advised that it was already finished and told them what else was suppose to be done. The manager Chris is refusing saying I never took warranty cover. Joe the salesman told me if the car gave me mechanical issues within 6 months they would sort it out. I’m now stuck without transport to work while my car is filled up. I’m being told I must sort it myself. So in actual fact Dekra issued a certificate without doing checks of which is a concern considering how many cars they let pass. Are we safe on these roads? They thought the 6 months would pass without the issue surfacing but little did they know I was going to frequently do long distance.