Where do I stand?

I traded a car into a dealership that I owed $1800 and asked for that balance to be added on to the end of the balance on the new car I was buying. Long story short everything went through i signed papers saying they would pay off the 1800 balance. Exactly one week into having the car I took it back to the same dealership to have a service appointment I had made, done. (I was under the impression they were changing the oil, topping off fluids etc.) They called me after having the car for 8 hrs and said the transmission wqs bad and the driver side airbag didnt work and that it was going to cost more than the car was worth. They told me they couldn't let the deal go through because of the major issues. They scrapped the whole deal and said I don't owe them anything. I guess my question is can I hild them responsible for the 1800 since I signed a contract saying they would pay it off? Or can I make them fix the car and let the deal go through? I'm just confused on what to do...