My money is on the compressor - either it has shat itself or the clutch is not engaging.

And from your original picture question, the first plug is the only one that connects to the aux fan. If you jiggle the second one around you'll find it pops out and has no electrical connection to the aux fan at all - it is a sensor and is only clipped into the aux fan by plastic tabs

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2004 E53 4.4L N62