How wide are your rows and columns in pixels? Because the way you called the constructor in your Board class...
Car_1 car1 = new Car_1(1, 1, 0);
Car_1 car2 = new Car_1(1, 2, 1);
etc.
you have each row and column set to 1 pixel, which is really small.
You should space out your cars for each row. Like this if each row was 50 pixels wide.
Car_1 targetCar = new Car_1(49, 99, 0);
Car_1 car1 = new Car_1(0, 0, 0);
Car_1 car2 = new Car_1(0, 49, 1);
Or if you can't that or collisions to work, you could leave the constructor calls as they are and make your board out of an array, but that would require making more pictures (breaking up 100x50 pictures into two 50x50 pictures for each car and another picture of each square for each direction it would face) then you can display each square one by one.
Just a few things to think about, I hope that everything turns out alright.