@rappin9 ,Rodney, The charging port on a GoPro 3 can be repaired or replaced. This is really not a repair for the inexperienced because the charge port for your device is soldered to the mother board and the heat generated could cause further damage if not very careful. I will post a link to a tear down guide to get you inside the GoPro Hero3 to check the charge port and will also post a link showing what is involved in repairing/replacing a mini USB attached to the board. The last link is to new charge port, which you can also do a search for better pricing perhaps if needed. If not wanting to do the repair yourself have a good computer/cell phone repair shop have a look and estimate repair. Good luck.
I hope this helped you out, if so let me know by pressing the helpful button.
[guide|12457]
https://www.youtube.com/watch?v=tLgm3L1UqPo
http://www.ebay.com/itm/Gopro-Hero-4-and-3-3-Main-Board-Mini-USB-Data-Port-Replacement-Repair-Part-/301796049860?hash=item46447243c4:g:JfoAAOSwo0JWQvn6