That is certainly a tough case. You didn't mention any injury and if you only have property damage, you will probably not be able to find an attorney to assist you. I would suggest if you believe that you were not at fault and if you don't have insurance to pay your property damage that you bring suit in the magistrate court in the county in which the other driver lives.
The above is just my opinion based upon the limited facts provided. It is not intended to be offered as legal advice nor is it intended to establish an attorney client relationship. You should seek a consultation either in person or over the phone to discuss any legal issue that you may have raised.
Yes you have a possible case, but, proving is could be difficult. It will be your word against the other driver's word. You should report the incident to your carrier and to the other driver's carrier stating your case.
Report the incident to your insurance carrier. Give them all of the information, including witness names and phone #s. Let your insurance company deal with the other driver's insurance company.
Report the crash to your insurance company and given them the name of the witness. This is a hard case.
DISCLAIMER: David J. McCormick is licensed to practice law in the State of Wisconsin and this answer is being provided for informational purposes only because the laws of your jurisdiction may differ. This answer based on general legal principles and is not intended for the purpose of providing specific legal advice or opinions. Under no circumstances does this answer constitute the establishment of an attorney-client relationship.