i think the laptop has a physical problem probably with the mother board. its possible its with the battery or charger but they tend to fail totally rather than this way.
the usb thing is interesting but i dont know that it is really significant. it is the motherboard that is sending the power to the usb port and if that is broken it can be doing anything. For instance my laptop shuts down the usb charger even when it goes into sleep mode though it is certainly getting power to the laptop. it may be designed to send all power to the led when its broken so it doesn't necessarily mean that the laptop is not getting power. just that its got a serious problem physically.