Dúvida sobre won't

Porque se diz: "The computer won't start" e não "The computer doesn't start"?

Both are good for most situations. They actually mean the same, Although the first sentence seems like the future tense (Will Not), and the second sentence is in the present tense, they actually both refer something that is happening Now. The car will not start is like a prediction, I know that the car will not start. But, we use it in the present tense sometimes as describing something that is happening now.

Also, the computer is not starting is the same as the computer will not start or does not start.

The car is not starting, the car will not start, the car does not start. All carry the same meaning in spoken English.