I have two things to say:
1.) You say that the car did not run when she came to pick it up, and yet she handed money over to you. So in my opinion and hopefully the opinion of any reasonable person, she accepted the risk right there that this car may not be in working order.
2.) Quotation from NYS Lemon Law
ARE PRIVATE SALES COVERED?
No. If you bought your car from a private individual (rather than from a dealer) you are not protected by the Used Car Lemon Law. You should consult a lawyer for advice as to other possible remedies. If the purchase price was $3,000 or less, you may wish to pursue your claim in Small Claims Court.