You have a medically compelling need for true silence, and I suspect that there are some alternatives that you might want to consider.
If space is not a concern, and neither is money, you might want to consider something like the Zalman fanless case and just start with that.
If that is too noisy, you might want to build a solid state cooling case that uses powerful TECs (multiple 200W pelts) for cooling. Take a normal case and computer and enclose it in a handbuilt sound deadening enclosure so that only the CD/DVD drive is exposed. Watercool TECs on the CPU and GPU and run the radiator passively outside the second case. Watercool some other pelts that cool the air (using fans to move the air across normal heatsinks on the cool side of the TECs). So, you have fans and noise inside while you have a hot radiator(s) outside. Use radial transmission coolers like the Zalman passive cooler (ebay is cheaper than them). Expensive? Oh yeah. Expensive to run, too, as it will eat power faster than you can believe. But, it will be very quiet.
You could also use the Zalman case a base and TEC cool it's exterior while dumping the heat to some appropriately large radiating surface.
Dunno. I feel for you, bud. Maybe just put your computer in a closet, duct air outside and run cables to a quiet monitor and keyboard? Might be cheaper and still save your sanity.
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