Sorry to hear about your car dying, I know it can be a pretty sad day when that happens. It sounds like your car met the same fate as the only car I've actually managed to kill. I would say that it's likely that your motor over heated, and chances are that the heat caused cylinder damage and you lost compression. When this happened to mine, I could get the motor to turn over, but I couldn't get the car up past about 5 mph, blowing smoke the whole time. Basically, without looking at it, I would venture to guess you need a new motor.
Now this begs the question as to whether it's worth it to put a new motor in it. If the car is newer and still worth some money and the rest of the car is in good shape, you might consider a new engine. It will cost you several grand most likely, though you can probably find a re-manufactured one. If it's an older car, I'm talking 10+ years old, with over 150,000 miles, or it's just a crappy car that's about had it, then junk it.
As for getting financed, you need to be 18 to get a loan. However, banks will likely look at your assets, your income and your credit rating. If you have never had anything that would help build credit, like a credit card you pay off every month, or even a phone bill, then you probably have no credit. In the bank's mind, you are a higher risk. In that case they will likely not give you a good interest rate and or may require a co-signer. In that case a parent can sign.
Speaking of financing, you'll have to pay attention to interest rates (APR) and the length of the loan. For example, a friend of mine just bought a 7 year old car, with a 72 month (6 year) loan at a high interest rate, and the car had almost 100,000 miles upon purchase. That was incredibly dumb of them, they will be upside down in that loan really quick and chances are that the car won't last 6 years and they'll owe money on it long after the car dies. Keep in mind that the average life expectancy for a car is about 13 years or 150,000 miles. After that, you're riding on borrowed time.
If you can put a down payment on the car, banks will look at you more favorably, and probably get you a better interest rate. In terms of interest rates, in my opinion, heres' what to look for: under 5% interest, very good, 5-9% acceptable, 9-12% bad, 12%+ and you are getting screwed. You may also consider looking at financing from a dealer, if you are buying a car from a dealer that is, as most dealers do financing and if you can't get it from a bank, most dealerships will do everything they can to get you financed.
Anyway, hope this helps.