I'm not sure about the Hero4. Is there anyway to reset it? If yes, this should be tried first.
If there isn't a way to reset it, or reseting did not solve your issue, then can you place a known good charged battery inside your GoPro and see if it works.
- If the GoPro works with a charged battery BUT does not charge, then either the charging port or the charging circuit on the board are damaged.
The charging port is a pretty straightforward repair that nonetheless requires a professional with the right tolls and skills.
The charging circuit, now that's a different story.. special skills and tools are needed also, and the right type of experience in trouble shooting fixing those things.
- If your GoPro does not run on a charged battery, then something in the board's circuit has been damaged.
Repairing a faulty board that doesn't start is not straightforward; and finding and fixing the issue will rely on the skills of the repair tech and the extent of the damage.