Your no-fault coverage is for the medically related expenses, for you and your passengers. It doesn't have anything to do with repair of your car. And generally speaking, the no-fault policy in Michigan is aimed to minimize excessive pecuniary litigation (for example, suing the at-fault party for loss of wages, or any out-of-pocket expenses, etc).
Because the other driver caused the accident and was "at fault", you should file a claim with his insurance company, not yours.