An unsigned will is not valid. Unfortunately, it will be very difficult to contest the will based on the limited facts in your question. I recommend you contact a local attorney, possibly the one your father used to see if there is any evidence of fraud or duress that might negate the last will and then your sister and yourself might inherit under your state's laws of intestacy. good Luck!
First, I'm sorry about your loss and the stress that this situation with the old will and draft are causing. Unfortunately, the unsigned draft doesn't give you any standing in NC. The court will probate the signed will. While you may be correct that the neighbor took advantage of your father and never read the draft to him, there is nothing which can be done implement the draft. However, please take note, if the 1999 will does not specifically mention the disposition of the real estate, stating that such real property specifically goes to certain deviseees, then by NC law, Statute, 28A-15-2(b), it would belong to your father's legal heirs, presumably, you and your sister, not the neighbor. I would recommend that you seek formal legal advice.