You didn't receive papers? You should be talking to a lawyer about reopening the case.Go to the court where it started. Look at the paperwork they have on serving you. Get copies and get a consultation from an attorney. If you weren't at fault and it's less than 3 years ago you may want to have your own case, so contact a member of the NY State Trial Lawyers Assn--they give free consultations.
Boyer is right, if you want to wait 5 years for your license. If you want to deal with this now, you have to bring a motion to vacate the judgment. Once vacated, DMV will restore your license. I have had success with these motions in the past.
You can retain an attorney to file a Chapter 13 Bankruptcy, which will allow you to pay the money over a 60 month time period. Good luck.
