I have not seen the wiring diagram of this car but going from the symptom you describe, you say the engine was idling high and fan was running, this indicates that the ECU had pulled the idle up to compensate for compressor load. But compressor was not working.
It leads me to believe the ECU was commanding correct - you could have verified this from simply switching the AC off. It is very unlikely the A/C compressor is directly controlled by the ECU. In the worst POS design cars there would be a relay to energize the magnet coil and a fuse in between too.
Lets take into consideration the ECU is somehow commanding the system like an older mitsubishi - there would be a fuse between the line to protect the ECU.
In this case, you check the resistance of the coil to determine if the winding is open, you check the clutch gap to determine that its leaving contact on heatup, you check the system temperature to isolate the overheat kill being activated.