What has apparently happened is that the other driver (now recognizing that having a fully chargeable accident is likely to impact his insurance rates) has changed his or her story, and now denying liability. His or her insurer is now offering half of the damages in the hope you'll take it, go away and so they will be ahead $1,500. You have 3 alternatives:
1) Take the $1,500, save yourself the hassle, and eat a $1,500 loss.
2) Sue the other driver in small claims court for $3,000 (assuming the amount you can sue for in the local small claims court is that high). If you sue it's almost certain the other driver will report the suit to his insurer and what likely will happen next is the insurer may make you a somewhat better offer if you'll agree to withdraw the suit, as otherwise it has to hire a lawyer to defend its insured.
If you don't accept its higher offer and continue with the suit at the trial you will need to be able to prove both that the other driver damaged your car, and the damages to your car really are $3,000 which will require you to provide evidence that is admissible in the small claims court. As I am not a NV lawyer and don't know the rules in NV but if the repairs were not completed so you can't produce a paid repair bill, you may be able to be show the cost to repair the car using a written estimate or two, or you may have to bring in a mechanic to testify that the cost to repair the car is $3,000.
As to whether the other driver was at fault, if you don't want it to be just your word against his, you'll want to have at least one and hopefully both of the 2 witnesses who heard him admit it was his fault in court with you to testify what they heard him say. (They didn't have to witness the accident itself to testify as to what he said.) The defendant's lawyer likely will try to show possible bias by pointing out that the witnesses are your friends or co-workers, but if they seem honest that will carry great weight with the judge, and judges generally can tell when someone is lying. The other side's lawyer may try to argue the accident was partially your fault (such as if you parked your vehicle improperly, or it was moving) so blame, and damages, would be apportioned, so be prepared for that.
3) Consult a local lawyer who may have yet a better idea (and be prepared to pay the lawyer for his or her time as I'd doubt any competent lawyer who is not a close friend would take on a small property damage claim on a contingency basis). The lawyer might know the insurance company, and might be able to make a phone call or write the type of letter that gets the insurance company to give the matter serious reconsideration. While a local lawyer is the best bet, if it's not up your alley and you are confident you will be able to prove the extent and cost of damages to your car, I'd file suit in small claims court and see what the insurer does. I'd bet they raise their $1,500 offer by 50% (to $2,250) so they don't have to hire a lawyer plus take on the risk of paying out the full measure of damages in addition. Given that the small claims filing fee is far less than $1,500 it's a relatively low risk way of proceeding. But my best advice would be to speak with a local lawyer. (Sorry I got the amount at issue wrong in my original answer, which I have now edited to correct the amount of damages and the insurer's original offer.)