Help on Car Accident

I had a car accident at a 4-way stop sign one week ago. A careless driver didn't stop at the sign and hit my car on the passenger's side and damaged two doors.So far, he hasn't reported this accident to his insurance Geico. Geico said they won't accept the libility unless the police report is easy to determine whose fault. And they still may decline the liabilty. My insurance appraisor said it's not a total loss, while the Geico's appraisor said it is. And my insurance can't cover my car rental and medical.

How can I handle such a problem? I just don't want to waste too much time on such a simple case. Shall I have to talk to a attorny? Many thanks.