I have done some calculation on the noisebox idea.. and found out that you need at least 50 cfm (2 panaflo at 12V, or one 120mm) airflow. Then you still get 5C temp raise for a medium power usage system. And on top of that you would need some adjusting fans to prevent too much under- or over-pressure. Therefore its almost necessary to use watercooling in combination with the box to make it useful. Otherwise you might need to increase cooling and noise inside the box and its Status Quo.
I have also whacked my brains on how to cool a box without aircooling. But there is no real efficient way. Acoustilock, as MikeC linked, has a heatpipe aircooling system, completely passive and airtight. But that box is like $5000.
(Sideparagraph. Please skip if bored.)
One of the more whacky ideas I have is to have the computer in a compressure chamber. Law of thermodynamics says that you need more energy for more pressure. So.. you could prevent tempraise of air by applying increasing pressure with temp raise. Problem is that you have to vent the system eventually, secondly I dont know what high airpressure does to computer components.
In effect you would have a computer dead silent.. but a huge strange contraption of metal, with a compressor that makes noise.. and some 'steam engine' type of sounds every minute or so when the pressure valve opens.
(End Sideparagraph)
I think.. the better solution to noise problem is, as silence-father MikeC says, to remedy it at the source. However.. you cannot completely deaden everything by just buying the right products. Because of that, and if you like to do handywork, one might benefit from doing custom work on parts indivudially.
I think you can do alot with making your own HD silencer. You can buy them of course but they are expensive and use up more space then they have to do. If you, for instance, have 3 HDs you can fit them into one custom enclosure. Or you can try to inbox HDs directly at their mounting places.
You can also make ducts and mufflers here and there inside and outside your system. You can also build your own case which is more suited for low noise level.
What I do now is to have a box that just controls my airflow and noise paths. This combined with some furniture planning so that I try to minimize noise paths form my computer to me. The box has no extra cooling. Its just there to remedy the bad noise ergonomics of my case. A better case would be just as good. One advantage, however, with it is that it is easier and more efficient to put acoustic dampening material inside or outside this type of box than inside the computer case.
Alot of links I could post about what I have written. But too much work.
Search the forum if you want more detailed info about specific ideas.
