what does it take to prove that Iwas not at fault in a car accident.

during the end of the hurricane when traffic lights were inoperative a driver ignored the "stop rules" and hit my car at fairly high speeds while I had the right of way. The Police issued no fault tickets saying simply that he was not a witness and both of us drivers had a different account of the accident.I have pictures of the accident plus the fact that I was 2/3 through the intersection when other cars filling two lanes stopped to let me through except for this driver coming on the 3rd lane never stopped. The pictures shows the point of impact. She hit my car.