Inasmuch I agree with Shirin regarding the meaning of the sentences, we would normally use: 'The car won't start' , or' the engine is just not turning over when I turn the key'. Or, we might say that the car has broken down. It is less frequent that we ay that a car is not working.

the car isn't working means at the moment the car is not starting or working while you are trying to turn the engine on. the car won't work means you are not trying to turn it on at the moment but you already know if you would try, it won't work ( if you try the car won't work).