Random shut down when power adapter unplug. Time for a new battery?

Power adapter light will not light up hence battery refusing to charge at times. It’s a “new” OEM charger that I just bought thinking it was the problem. The adapter itself is also very warm/hot when battery starts acting up. Here’s my coconutBattery screenshot. I know I‘ll probably need a new battery but I was worrying that there are other factors since the battery hold it’s charge pretty well otherwise. Any suggestions or help will be great. Thanks!

Another screenshot when it’s unplugged from power: