HP laptop power problems

I have a HP Pavillion laptop about 1 1/2 years old. I am having power problems with it. When I plug it into an outlet to charge it, the green light on the power box is lite but when I turn on the laptop it will shut right down because the internal battery must be dead and it seems like its not getting power because it wont stay on when plugged into the wall. I was wondering if anyone else had this problem? I am assuming that the problem is within the power box and cord and not the laptop battery…Does this sound correct..