What happens if a car is totaled and there is no collision insurance and the other driver's insurer says fault is not conclusive?

You definitely need to have a lawyer involved in this case.  First, because the police report fails to indicate which car is at fault for the accident, you are going to need a judge or jury to make the ultimate decision as to who is and who is not at fault or whether there is a way to apportion fault and how.  the fact that you have not had a ticket or accident is not going to be proof of who is at fault in this case.  rather, the judge or jury will listen to each of your renditions of what happened and determine who is telling the truth and which party is at fault.  you want to have a lawyer represent you in this case to examine the evidence and testimony.  the problem is that the amount of money that you will pay for the lawyer is less than what you will recover unless you have damages for pain and suffering.  if you were injured, then you can collect more.  if you rather take the driver to small claims court and argue to the judge on your own, then you can as it may be the best thing for you economically.