You truly need to send that to Lenovo. It is truly out of order.
PS: Why would you try to fix it by yourself if Lenovo can for you? Maybe they will send you another laptop if the one you have is really broken.
What you can tell them is: "I can't turn my laptop on if I don't have it connected to a charger. I already contacted you for the same problem, but even if the battery was replaced, it still doesn't want to work properly. What can I do?"