The only other thing it likely could be other then the laptop is of course the power supply suggest you try to find someone with the same type of power supply and give that a try.
Could be the sensor wire on the supply and if so you could luck out by picking one up on ebay cheaply.
The odds are only so so as the computer should had come up with the battery unless the battery got drawn down.
How costly and how old is this laptop?
Second issue do you have anything only on this system hard drive that you need?