as above try another working power pack of a friends, if it is still the same and they have the same laptop try swoping the battery too, if it powers on with the other battery and no power pack great, then try with the power pack, if all works put your old battery in again and try the new power pack if it still works then it is your power pack. if it is still the same then chances are you have one of two faults, either a complicated motherboard fault or a simple internal power socket fault, as Kyle said above it is simple to replace, and you can probably watch a video of how to change it on Youtube.
If when you put the power plug into the laptop it is very slack, loose or does not stay in on its own, chances are it is damaged...