Emergency Furnace/Vehicle

I'm not the type of person who asks for help. I've always been extremely independent and even the thought of asking for help makes me uncomfortable. However, I've come to my breaking point and I do, in fact, need help.

In December 2013, my car was deamed unfixable and my insurance company was unable to help in any way due to the problem being "Mechanical." Within 1 week, my furnace began leaking carbon monoxide and was deamed unsafe for use and unfixable. Columbia Gas came out and turned it off and told me I needed to purchase a new furnace. 

I am a hardworking, responsible, mother of a beautiful little girl that was now faced with 2 major unexpected issues. Being that the weather was in the negatives, I spent my emergency fund for a down payment on a furnace. I'm currently still making monthly payments for the furnace and have now been without a car for over 3 months. 

I've written to the Attorney General in hopes of getting some relief of the $7,100 I still owe on my car from the dealership that sold it to me. The company is out of business and the Attorney General is unable to locate them. I'm stuck paying over $300 a month on a car that is unuseable. I have been to dealerships and explained my situation. I am just unable to put any money down or increase my current car payment by more then $50. 
Dealerships are unable to help me get into a car due to the amount owed on my current car and my financial restraints.

I have found a few used cars that seem to be reliable (around $2,000-$3,000) but I don't have cash in hand for private dealers. 

I've never been without a car, but this situation has put a very big strain on my parents (who have been wonderful helping me daughter and me out!). I work full time and I'm a single mother. I am fully relying on my father (who also works a full time overnight job) to take me to work in the morning, pick me up in the evening. The simplest tasks are a struggle of schedules. I am unable to take myself to the grocery store, doctor appointments or even take my little girl out to the park.

I am very greatful for my family and the help they've provided but we are now financially (and physically) exhaused and out of options. 

I just need a cheap, reliable car to get me from work to home and the grocery store until I am able to pay off my current car that doesn't work. 

I own my own home and pay all of my bills on time. I live paycheck to paycheck and do NOT receive any type of government funding. I just got hit with 2 major unexpected problems at the same time. Any help would be greatly appreciated by myself and my little princess.