2002 Cadillac EL Dorado Fog Lights

Does the green LED indicator turn on/off with a press of the switch. Do the headlights function normally, and are they on high beam. The fog lights will go out if the headlamps are on high beam.

No green LED would indicate most likely that the relay is not closing, or not being controlled. By assuming you checked all fuses, was one of these the fog fuse in the underhood fuse block? Swap the fog lamp relay with another of similar, there should be choices. The control side of the relay recieves power from the ignition 1 fuse, and is grounded by the Body Control Module. This grounding occurs due to a bussed message from the IPC to turn on the lamps when the switch is activated. If you know electrical, you could apply power to the lamps from the relay connection, the lamps and the indicator light should light. It is the purple wire from the relay, or terminal C6. If they do not light, you have a circuit problem beyond the relay. If they light, and swapping the relay provides no resolve, check for grounding from the BCM on pin D4 DK GRN/WHT. If the bcm is not grounding, it could be a faulty BCM, no bus request from IPC, or a faulty fog lamp switch, which is part of headlamp switch.