Remove the solenoid and test it, it can also be tested with a scan tool, under the hvac menu, the compressor activity is under special functions where you can see the amp draw of the solenoid.
You need to simultaneously see the liquid and suction pressure as the solenoid takes the full 1 amp draw.
If its not then the solenoid is not functioning, you can find a replacement if you are crafty enough.
The way this system works is that the suction pressure is maintained slightly above freezing point (verified by evaporator thermister reading and target temperature delta) - both are seen through scan tool. While the solenoid idles down to 0.4 amps or lower, the system immediately reacts to changing rpm or temperature and is seen as solenoid amp change and verified by gauge manifold. The condenser cooling fan control on this corolla has a module to control rpm and its done by engine ecu which also takes evaporator and liquid pressure data from the ac amplifier.
The one very important factor that dictates good functioning of such system is that you need to use a good vacuum pump and pump down the system to about 500 microns and leave the pump running for about 20 minutes to ensure complete dehydration of the system. Once a good vacuum is pulled then the exact refrigerant amount is installed, a low charge or overcharge on such compressors never work.
