A common occurrence in laptops is the power jack breaks on the inside of the laptop. The more often the cord is plugged in and out, the sooner the jack will break. If you are adept at soldering, it is one of the few things easily repairable on a laptop's motherboard. If DIY repair does not seem feasible (look on youtube for videos on DIY), there are quite a few companies that specialize in laptop power jack repair (it's that common).
I would say off hand that is the issue here
edit: If you have a multi-meter, you can check to see if the power adapter is putting out it's 19.5v (or 22v or whatever)