When I plug the adaptor into my Dell XPS L702X, the notification light does not come on. The battery icon shows "Charging" and a percentage but never actually charges. On the odd occasion when I plug it is the notification light will come on and then the icon shows "Charging" and the time left until the battery is fully charged. But that is seldom. Could this be the charger/adaptor or is it a fault within the laptop? Thanks.
It could be both. From my past experience, it is usually the issue with the adapter but not the laptop. If you go to a repair shop, they will probably test it for free for you.
Also, old dell laptops have this sort of issue with Windows Power Management where windows refuses to charge the laptop. Testing with linux on usb will help you be more certain.