It's possible that the issue with the camera's back buttons not working is due to a problem with the circuit board or a software issue. If the connector and flex cable are both in good condition and properly connected, then it's likely that the problem is not with the cable.
One solution you could try is performing a factory reset on the camera to see if this resolves the issue. If not, then it may be necessary to take the camera to a professional repair service to diagnose and fix the problem.