With regards to the battery , all new batteries on anything don't work properly until they have been charged a few times. You should always let rechargeable batteries on anything run low before putting back on charge. This is because charging a battery pack before they are fully run down causes cell blindness. In the case of a laptop you have to be more careful though because something might go wrong if you let the battery go too low. EXAMPLE .. I used to fly radio control planes and if a cell goes blind you loose radio contact and crash. In the case of drones though , they detect low power and return to base.
ok so back to the laptop ,you say its new so you need to reject it as not fit for purpose or go to the shop if possible and demand a replacement asap , if you got it from a certain high street chain you must go ASAP because after a certain number of days that can insist on repairing it instead of replacement.