Sounds like to DC Power Jack. This is a common problem with laptops because as you insert ther power cord it moves slightly the jack which is soldered on until eventually it breaks away or sometimes the contacts wear so you get little or no circuit. Either way you will need to either replace the jack or repair it. If you are handy, once you have aquired a new jack, it's a complete strip down to get the motherboard out remove the old damaged jack and solder in the new one.
In some cases you might just need to resolder the jack's points if there is no visable damage.
If you have not done this before there are a lot of screws to remove to access the motherboard and you might want to draw a diagram as to where they all fit as they are not all the same colour, size or thread.
Ken (ATAC Comuters Ltd)
May 2009