Charging ports on laptops go bad all the time. If you aren't experienced with working on laptops it is probably something you will have to take to a technician.
However are you sure it isn't charging? There will be a pin in the middle of your charging port. You can carefully nudge it to see if it moves. If it does, even a little, that is going to be your problem. You can try removing the battery and plugging it in. Sometimes defective batteries will cause strange problems.