As an IT expert, I am surrounded at all times by whirring fans, except when I am driving, in which case rumbling motors. These fans are to keep the electronics cool enough to function. While there are replacements, such as watercooled systems, that are significantly quieter, such systems are always significantly more expensive.
However, sound is ultimately a waveform, and interferes with itself destructively. A +1 and a -1 waveform will, when put together, combine to form 0. You can buy noise cancelling headphones that work using basically such a principle -- a microphone records the current sound, a microchip inverts the signal, and this is played into the headphones, cancelling the current sound. This gave me an idea to make computers quieter.
Instead of one case fan whirring away, there would be two rotating in opposite directions. The noise they produce would have opposite waveforms, cancelling each other and making the computer very quiet indeed. A small bubble of space between them would have higher than normal pressure, and a vent would be requires to shove this air out of the way. The case would then have negative pressure, and slowly suck air from the room. Filters would be required in the case to prevent dust buildup on the electronics, which is somewhat of a pain in the neck to clean. (Dust interferes with thermal transfer.)