Translation:
My car is e36 325i sedan of analog climate control.
My car is an E36 325i sedan with the analog climate control unit, i.e., the standard one with the rotary knobs that was installed in pre-1996 models.
As the Key was set on, all buttons(a/c, re-circulation and rear defroster) on the climate control is lightened but can't be off.
Whenever the key is turned to the ON position, all the LEDs on the climate control buttons illuminate, and even if I press them, won't go off.
Strangely, the compressor is engaged if auxiliary fan relay was removed.
Even with the auxiliary fan relay is removed, the compressor still turns on.
Is this electical problem or other parts??
Does this sound like an electrical problem, or is it due to a different reason?
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Questions for the original poster:
(1) What year model is your car? This is important.
(2) What is the climate control doing when you turn the car on? I mean, aside from all the lights being on, is the air blowing out at full blast? Does no air come out? Hot? Cold? We need details. We are trying to diagnose your problem over the internet without being able to to see, touch, or hear your car.
(3) Is the A/C compressor constantly on? Or only at times?
Removing one fuse guarantees nothing with the climate control system. As you may already know, relays 16, 20, 23, 31, 37, 39, and 41 (which is the one you removed, I am guessing), all affect the A/C system. The compressor is controlled by the A/C compressor relay (#14 in the relay panel in the engine bay). Removing this will certainly keep the compressor from coming on.
It seems to me like your problem is with the climate control unit itself. However, we really need to know more details, or otherwise, like darkhorse said, we may give you wrong advice.
you have two possible A/C systems: the IKHA & the IHKR configuration.
I am guessing he has the IHKR :dunno