Get an attorney! You will be filing a claim against your own insurance company but don't be put off by that. Also, it doesn't matter what the cop's think or the insurance company thinks. It matters how well your attorney can represent you...either in court or leading up to court. Also, be prepared to sue your insurance company. It's often the only way to get them to pay what is due to you.
It appears you have evidence that the other party was driving with their lights off. That is a good starting point for any attorney. Oh, and don't be dissuaded by what you hear from some folks here. They have a habit of telling everyone they are at fault and have no case.
This is why you have uninsured motorist. Good luck!