quiet PCs

No - the panels in a cheap case can rattle from hard disk vibrations - a little square of dynamat kills it quick.  Better cases with grommet-mounted drives generally have sturdier panels that don't ring like cheap cases.

Maybe I wasted money, but I just ordered the dampening installed in a sturdy case. Anyway, I am not going to test whether it changed anything by tearing the dampening down...

And runaway, you are more than right - in addition to joints there is a lot of unprotected surfaces left, fan openings in the first place!

Don't get me wrong - the answer is a combination of all the contributions on this thread.

Either buy an expensive ready built case
OR
Stop cheap sides from vibration with dampening
NoiseLess fans (read not cheap)
Noisless CPU Coolers
Video cards with no fan
OR
Water Cooled 

Well, I did No.1 (I assume that you mean a computer case, not an additional wooden case=cabinet) plus No.2 (but quiet, not noiseless fans and cooler). At this point please refrain from telling me what I did wrong, the order has been placed and accepted, and I might frustrated ;-D

Don't get me wrong - the answer is a combination of all the contributions on this thread.

Either buy an expensive ready built case
OR
Stop cheap sides from vibration with dampening
NoiseLess fans (read not cheap)
Noisless CPU Coolers
Video cards with no fan
OR
Water Cooled 

The one critical thing you left out is to isolate the hard disks from the case.  I did it with a DIY contraption some years ago

but have since switched to cases which grommet-mount the disks.

Good point I forgot to mention those grommets also important

PQ there is no right and wrong just better choices 

I did exactly the same - best quiet case I could afford and best fans (3) I could afford (case came with grommets)
Are there quieter cases & fans ? probably but everything is relevant.

I'm sure you will be happy with your purchase.

If you have to have the damned PCs in the room with you, I don't think that there is any absolutely quiet system - but quite a few are quiet enough.

I have a nearly-finished version of something similar to WildDuck's wooden box, only mine is a somewhat modified 19" rack unit with a  labyrinth for the cooling fan air feed in the base, and a rather substantial transparent closing door over the front, with seals (that's the bit I haven't finished yet) and double-walled sides. It's going to get both rack-mounted DAWs in it when it's finished, and no, I don't normally run both at once so I might get away with it as far as noise is concerned - we'll see later in the year.

Typing this has been rather difficult, because I'm doing it on the Flying Scotsman, and it shakes about quite a bit at speed. It has free WiFi though, so I thought I'd give it a go.