Yes you will need to replace the battery. Since you are able to use your laptop when it is plugged-in, it is a great indicator that your charger adapter is not the issue. Make absolutely sure your computer is turned off. Remove the back cover of the laptop by unscrewing the screws and gently lifting the cover up. Locate the battery which is usually a relatively large rectangular shape device and replace it with a known working one. If this does not work, there might be an issue with the actual wires inside the laptop. If that is the case you will need to either send it back or see if a local electronic store can do something with it.