Hit-and-Run driver now says I hit him after he told police he wasn’t aware of any accident and his insurance isn’t covering my car. Options?

The police report should support your version of the incident. I would recommend that you go through your insurance company and let them work out settlement with State Farm.  I am presuming you have collision insurance on your car.  USAA will pay for damages to your car, less the deductible.  If they are successful at getting State Farm to reimburse them for your damages, you will get your deductible back. If they only get a percentage of reimbursement, you will be reimbursed the same percentage.

When you speak with USAA be sure to tell them there is a police report on the incident.  I presume you have confirmed with the police that the other party told them he didn’t know there had been a collision. 

If there is no police report, or if the report disputes your version, you may be held responsible for the collision since it appears the damages are the rear of the other person’s car vs the front of your car, which implies a rear end collision on your part.