You'll basically be looking for a car that's $10k or less and a 60-72 mos contract. It's possible to do no down payment, but not likely. Try looking at carvana. You can pre qual on a soft pull and it will give you an idea of what you should be looking for along with expected rates, down payments and contract lengths. When I was shopping, they actually were giving me better rates than cap1.
Even if you don't want to keep the car, you should find a used transmission online and pay a shop to put it in then sell it.
If it costs you $1500 to do this but makes the car worth $5k again instead of $1k, you will have just saved $2500.