Batteries are allowed, but they have to be installed in the device. If it is installed in the laptop that's fine, if it's just in the box with it and not installed, that's not allowed.

You will not be exempt from paying duty on it just because you are carrying it with you. You may choose not to declare it and take your chances, but that doesn't change the fact that duty may be owed on it.

That being said, while you can put it in your luggage, it is easily one of the stupidest things people do. It won't be covered should something happen, there's a very good chance it will disappear or get damaged (not just the TSA, lots of people handle the bags on both ends, and any lock on a bag is a joke if people want to get into the bag).

I would find space for it in your carry on. Pack the box and cables if you want, but the laptop itself should never be sent as luggage. There has to be something you are carrying on you can check if space is an issue, laptops don't take up very much room.