The tentative answer is that, unless you were under the influence of drugs or alcohol when the accident occurred, you should be able to discharge this debt without much trouble. You will also need to have the judgment lien avoided.
Several of my former clients have discharged debts arising from their failure to maintain insurance. All of them have indicated that they regained their driving privilieges either after filing or promptly after their discharge.
I recommend that you consult with a bankruptcy lawyer in your state. Your attorney will need additional facts in order to advise you.
An useful resource to identify lawyers who represent debtors in bankruptcy is www.nacba.net. It is well worth the fees for the basic bankruptcy and the motion to avoid the lien to have the peace of mind that this was done properly. Good luck.
Most car accidents, other than DUI and deliberate torts, are dischargeable in bankruptcy. Usually the discharge lets you get your license back. So if you otherwise qualify to file, a bankruptcy may assist you with your license as well as eliminating the judgment. Feel free to call me to discuss details.