I am not a recording engineer (though my father was) but I suspect the more pragmatic approach to a quiet PC for your recording studio is to just put it in the next room and drill some holes through the wall for the cables.
True. Less radical thing I've done is placing the main unit next to heavy furniture in some distance from the actual desk, so it is mostly obscured for vision and sound waves it seems. With cabling and USB hubs (including those in the monitors) it remains pretty convenient. I'm sure you can go even further with standard sound dampening tricks if you care.
