Document everything for future purposes. Unfortunately, if you do not have insurance, you will have to pay for your own defense. At this time, I would talk to a wills/estates attorney to discuss protecting any estates, or seeking advice about which assets are protected.
Since you state you were not injured, it is presumed that the case you want to pursue would be for damage to your vehicle. In such instance, and assuming a finding of liability against the other driver, you would be entitled to recoup the cost of repair or the fair market (book) value if the car is totalled. Depending on the age of your car, etc., if the property loss claim is $5,000 or less, that is the probable reason why you can't get an attorney to "take your case", nor should you want to pay attorney's fees for a case of limited value. Go to small claims court without further delay.
This is why you pay an insurance premium, so your insurance company deals with the aggravation. If you pay premiums year after year and refuse to submit a claim when you have one, then you are throwing your money away. Cancel all your insurance except liability and save your money, and use the savings to hire your own lawyers and pay for your own repairs. My guess is, you will pay way more than if you just keep your insurance and submit your claim. But if principal is more important to you than money, you gotta do what you gotta do to be happy.