C4 means the thermistor on the liquid pipe at the heat exchanger is not reading what the board expects. That sensor reports the refrigerant temperature leaving the indoor coil, and the board uses it to control the expansion valve and protect the compressor. A wrong reading makes the system run badly, or stop, depending on which way the sensor has failed.
These sensors are a small bead on a lead, clipped to the pipe. They drift with age, and a drifted sensor reads a temperature close enough to look normal while being wrong enough to upset control. It is a low cost part, and replacing it is far cheaper than the consequences of the bad reading it produces.
The thermistor lead runs back to the board and plugs in. Heat, vibration and moisture at the plug change the resistance the board sees, and the board cannot tell a hot pipe from a bad connection. The plug and the lead are inspected before the sensor itself is condemned.
A sensor can fail open, fail shorted, or simply read outside its tolerance. Each looks different to the board. Open and shorted are easy to confirm with a resistance check against the temperature. Drift is harder and usually gets confirmed by comparing the reading against a known thermometer at the same point.
The sensor is unclipped from the pipe and its resistance is measured against the ambient or pipe temperature, then compared with the manufacturer’s table. A reading well outside tolerance confirms the sensor. This also catches a sensor that has come away from the pipe, which reads air temperature instead of pipe temperature and causes exactly this fault.
The plug at the board is reseated and inspected for corrosion, and the lead is traced for damage along its run. Resistance is measured at the board end as well as at the sensor, so a difference between the two points identifies a lead problem rather than a sensor problem.
A thermistor can read correctly and still produce a C4 if the pipe it is clamped to is not seeing normal refrigerant flow. Blockages and low charge change pipe temperature in ways the board reads as a sensor fault. Once the sensor and its wiring are cleared, flow is the next thing to confirm.