It could be either or both. If you have an electronics shop you may be able to get it tested before buying a new one. If that turns out to be fine, it should then be the socket itself. Sockets can also be easily repaired with a bit of solder and a steady hand. I would rule out a faulty battery because wheather or not the battery works, the laptop should get powered from the charger. Even if that is the case, removing the charger and pluging in the power should allow the laptop to start.