A/C Switch & Compressor Clutch Relay
WARNING: This page does not describe the selected car, but rather 7 other vehicles, including the 2002 Mitsubishi Montero Sport, 2002 Mitsubishi Montero, 2002 Mitsubishi Mirage, 2002 Mitsubishi Lancer, and 2002 Mitsubishi Galant. However, it is still accessible from the selected car via links, so may be relevant.
Using DVOM, check A/C power supply voltage from ECM/PCM. Turn ignition switch to OFF position. Disconnect ECM/PCM connector. Turn A/C switch and ignition switch to ON position. Measure voltage between ECM/PCM A/C power supply terminal and chassis ground. If battery voltage is not present, check and repair circuit(s).