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A more sensible and affordable solution is to simply design a quiet PC based on current off the shelf parts. These systems make just enough noise to let you know they're running and they don't cost all that much extra.
The case, power supply and motherboard are the foundation of any system. Lian and Antec are two PC case manufacturers we like. A number of their cases are well designed with ample airflow and are easy to work in without any sharp edges. Look for denser materials and rubber grommets that dampen noise.
Next, the power supply should offer plenty of clean reliable power without generating much noise. PC Power and Cooling makes quality supplies. Other manufacturers we've had good results with include, Antec, Enermax and Seasonic. A good rule of thumb on power supplies is go heavy and go steady. You'll pay more for a quality power supply but it's worth it. And good supplies will come with at least a 3-year warranty. PC Power and Cooling's warranty is five years.
Next, The motherboard design and CPU will have a significant impact on power consumption and noise. ASUS has a line of motherboards that use heat pipe technology to cool the chip sets. This eliminates one source of noise. AMD's Cool and Quiet CPU technology helps regulate the power consumption of the CPU and results in a cooler and quieter PC. The improvement is dramatic over Intel's current offering. A smarter motherboard and CPU combined with a better cooling fan such as those offered by Zalman keeps things running cool, lowers power consumption and reduces the noise output of the PC.