Help me save this dog

Hi there,

My name is Stephanie. My daughter Solana watched this dog get hit by a car and drove away. She brought him home in a lot of pain. The dog wasn't bleeding but his back legs don't look so good neither does his back. I've been looking for his owners. No one had come forward. I tried to bring him to an animal hospital they told me they couldn't take him unless I covered his medical bill. I called the non emergency Police, they told me there wasn't much that I can do about it. I can call animal control where the possibility is him being put down. I would really like if I can at least get him help to fix his legs maybe I can find him a new home. Please please please help me out! I'm willing to pay some it of pocket however I'm a single mom of 3 kids and already own 2 of my own fur babies.