No, this is a completely different use of 'would', and it has nothing to do with habitual action. Well done for making a good guess, though. In fact, here 'would' means that the car 'refused' to start, almost as if it had a will of its own and it chose not to start. It is the past tense of 'The car won't start'. In spite of its appearance, this is not a future tense - it means that I can't start my car. It's the same as saying 'My little boy won't eat spinach' - it's a refusal to do something. I can't force my son to eat spinach, and I can't force my car to start! So in the past, you say 'The car wouldn't start, so I was late for work.' I hope this is clear. This is a very common and natural use of the word 'would', but unfortunately many learners are unaware of it.