statute of limitation on filling suit against someone that damage my automobile on private property when the backed into my car

My son dropped my daughter off at her apartment. While waiting for my daughter to get out of the car, they noticed the neighbor, who is up in age and deaf in one ear, backing up toward the car. He blew the horn as my daughter quickly jumped back into my care to prevent getting her leg amputated. The lady hit the front passenger door hard enough to prevent the door from fully closing. The estimate we submitted to her was for $300.00 and the neighbor stated that she would pay when she got her check. Instead of attempting to pay, she changed apartments by moving to the next building and she stated that she needed to take care of moving cost and rental fees first. This has dragged on for well over a month with no payments.