computer Problem

So my laptop is a little over a year old. Today I was using it and it just shut off randomly. So I figured the power cable was not plugged in all the way and it just died. But no there is full battery. What is happening though is its not charging. It wont recognize the power cable being plugged in at all. I think maybe the cable shorted out or something and made the computer shut off. The port where you plug the power in though is very loose so I fear that that is where the problems lie. Any ideas?