If one is pulling, inserting the battery while the power is on, it could damage the charging circuit in the laptop. Since a new battery has not been tried, the battery is still suspect.
Here's the thing, clients never want to replace the battery. I can't tell why they do that but the battery does fail like this. If it's not the battery it's the motherboard or the power supply brick/adapter.
I don't see the age of the battery so I can't give a bigger nod to the battery. It's only a 300 cycle rated thing. At 18 months plus I have no qualms of trying a new one since motherboards are much more money.
My laptop battery has not been charging for some time now. I cannot seem to find anything that will correct the problem. I don't believe it is the battery because the issue started suddenly, and the battery was holding a good charge prior to that.
The last thing I did try was, while the computer was on and plugged in, I removed the battery, then replaced it. It indicated the battery was charging for about 10 seconds, then stopped. I repeated the process and got the same results.
I don't know if this helps narrow down the issue for anyone. I would appreciate anyone's thoughts on this.
Thanks

Chowhound
Comic Vine
GameFAQs
GameSpot
Giant Bomb
TechRepublic