My Laptop Shuts Down When Connected to Both Battery and Charger

I've noticed that my laptop shuts down instantly whenever I connect it to both the battery and the charger at the same time. This issue doesn't occur when it's running only on battery or just with the charger. Has anyone experienced a similar problem or have any suggestions on how to fix this?

Note: I have recently replaced the battery two times. Once because the original battery was completely dead. I then proceeded with another replacement because i was not able to charge the first replaced battery, which worked until it has been discharged. Now I have a half charged battery which i can use, but if i plug-in the adapter to charge it, the PC turns off with a popping sound. On the other hand I can turn on the PC if i disconnect the battery and only use the adapter.

I tried most of the usual recommended procedures of holding power button pressed, or BIOS reset, or battery pin pressing, and so on...

I also replaced the DC in Power Jack charger Charging Port Cable Connector.

I visually inspected the motherboard, but i could not find any damaged piece.

Thanks in advance.