While there are some people that believe an entrepreneur should have a big stake in the company - most savvy investors don`t encourage situations where the entrepreneur`s personal finances are on thin ice. They want him/her to be able to concentrate on building the business.
For your specific situation, the primary questions I would have are:
As an aside, before you sell the car, I`d have my business plan pretty well completed. That should indicate the answer to question 1 above. If possible seek out the advice of a Veteran entrepreneur especially for confirmation of your assumptions.
I always tell people to make sure that they are "warm and dry" and that they don`t burn assets like home equity (and cars) that they might regret later.
Be creative - $1300 isn`t that much. You could start a mini start up (like mowing, painting, dog walking, etc) to make that much. At $10 an hour, that`s only 130 hours of extra work. I would delay your business a little longer and find another way to come up with the $$. If you sell your car and the start up doesn`t work, then you will be looking for ways to buy a new car.