I don't know if you have time for this, but could you go to your bank or credit union and get a loan, and then find a car that is being sold by its owner? I'm not meaning to diss used car dealerships, but they're not always known for being honest and giving really good deals.
I don't know a lot about NJ, so I don't know if you will absolutely need a car right away where you're going to be living. If you absolutely can't find anything now (although hopefully that won't happen) could you just rent a car for the move and then look for one later, after you have a job?
I hope everything works out for you. I understand both car problems and a lack of money, so I'm right there with you. It sucks, and it's very stressful to have to deal with stuff like this that comes up unexpectedly. Good luck, and keep us posted!
