Well you will know if the Compressor Control Valve is bad because when you are running the AC on Full Fan Blower and Recirculation, the Suction side will start getting higher and the Discharge side will start getting lower. Every Corolla I have fixed with this problem had a Suction side of 70 PSI and a Discharge side of 150 PSI. When I replaced the compressor or compressor control valve, AC works fine.
The Compressor Control Valve controls the amount of refrigerant entering into the compressor. Because your Corolla has a Variable Capacity Compressor, the compressor is always running 100% of the time. The Compressor Control Valve controls the refrigerant from entering and leaving the compressor, and is actually like a solenoid switch. At full pressure/full AC pumping, the Compressor Control Valve is fully open; When the evaporator is very cold, it closes slightly to control the refrigerant gas circulation. The biggest problem is oil sludge gets into the Compressor Control Valve ports and clogs them up, which causes them to stick either open or closed slightly.