Can i get a car loan with a 590 credit score?

I Know, I know... its awful... I was a dumbs$$ for a lot of years. But I am doing amazingly better now. I have paid off my credit cards all but completely, I owe $300 on one and that is it. Paid off my car. And have been making regular and on time payments for a good few months. I just pulled my credit report and all my collections accounts have been closed, but they are still sitting on there ruining my score. My car is dying a slow sad death though, and i would like to get out of it before it totally croaks. Bluebook says that in the condition it is in its worth $1500 as a trade in, and I will have $600-$1000 as a down payment on a new car. I am looking at spending $8000 to $10,000 on a newer model used sedan. Am i off my rocker to think i will get a loan? I am prepared to have a higher interest rate, And will gladly pay it on time, and more then my monthly payment to help contribute to rebuilding my credit, but i dont want to walk into a dealership/bank and get denied completely. Do i have a chance?