Gopro HERO 3, the battery and cable are good but no power on at all.
Please go over the steps on: HERO3 Camera Will Not Power ON
Should it still be the same, please reach out to our Support Team.
They are available by phone or chat through https://gopro.com/help/ContactUs
Let them know of the troubleshooting steps taken.
If you have gone through the steps on the link and the camera is still not powering on, please contact our Support Team.