Injured in an Accident With No Insurance

I was recently involved in a serious accident in which I was injured. The other party backed out of his driveway and I struck him. I heard him admit to the Police that the accident was his fault. My problem is that I was driving my separated wife's car. The car did not run and I had recently fixed it. She had a valid insurance card, but I have since discovered that she had let the insurance lapse because the car was inoperable. I was seriously injured in the accident and required major surgery to my right lung from hitting the steering wheel. My question is whether the other driver is still responsible for my injuries under law?, And am I responsible for no insurance even if there was a valid insurance card in the vehicle.
Thank you...