Kobi C.
                                    2020.05.16 16:21
                                
                                
                                
                                    
                                    @Constanza 
                                     Good Question.
Yes, we would understand both sentences.
Native English speakers would make the following distinction.
1. If the owner of the car is thinking about an attempt to start the car either now or in the very near future, the speaker says: “My car won’t start.” because “won’t” is the contraction of “will not”
Example:
Person 1: “I’m going to be late to work today.”
Person 2: “Why?”
Person 1: “My car won’t start.”
Or
Person 1 (walks into a cafe): “Hello.  May I use your phone, please?”
Person 2: “Why? What’s wrong?”
Person 1: “For some reason, my car won’t start and I need to call a tow truck.”
In this example, she tried to start the car ( dry recent past tense)... the car currently does not start (present tense)... and she knows if she tries again (in the very near future) the car will not start without a mechanic fixing it.