A good way to check the health of your Chromebook battery is to use the Crosh utility. To open up Crosh, press '''ctrl + alt + t''' on your keyboard.
When Crosh opens, type '''battery_test''' at the crosh> prompt. This will start the battery health test. Since your battery is new, the health grade should be almost perfect. If it isn’t, then the battery will need to be replaced soon, if not refunded (if it is in fact refundable).
The power jack of the Acer Chromebook CB3-111-C8UB is soldered onto the motherboard, and is therefore difficult to replace. You could buy a whole new motherboard, but the whole process (motherboard, tools, shipping costs) may end up costing more than the laptop itself.