Did you tried to sync the NS Pro with cable? On the Nintendo Switch controllers settings (update 5) turn on "Wired Pro Controller Support", the controller should work plug'n'play without any config. If that doesn't work you should try isolating the possibilities one by one:
Disassemble the NS Pro and test (with multimeter):
- The battery;
- Test the energy port;
- Test the sync button;
- Check out the charger, try different ones;
Come back to report success or failure.
Thanks!