Some thoughts Faustus,
I think you should have put this under the general hardware section as it's about marrying many parts to get the quietness you want, and there is a bigger readership there.!
Everything is relative. If you're coming from an Evesham, I bet it's got 80mm case fans, a stock cooler/fan, a cheap, noisy PSU and a northbridge fan maniacally whirring away like a hairdryer at 6000 RPM!
Need to know if you are a big gamer/heavy overclocker type. Implication from the thread so far is that you are not. As said earlier, the key is the fans and 120mm is the way to go if possible. That can unfortunately mean a bigger (midi) sized case.
So on that basis:
Case: perm 1 of:
Antec 182 - nicely soundproofed, but heavy and not much fun to work on and I hated the door. I think the Tricools set at low are fine (everything is relative).
Lian Li V1000+ - surprisingly quiet, good cooling, light, pretty (IMHO), but expensive.
Akasa Eclipse - probably a good compromise on the above two, but not pretty (IMHO

)
Mobo: Gigabyte GA_P35C_DS3R - fanless, well reviewed, some future proofing, and relatively cheap.
CPU Cooler: Anything that can sport a 120mm fan. Scythe Ninja, Tuniq Tower for example.
GFX Card: I personally would steer clear of fanless cards unless you have absolutely no intention to game. I had one once, and the number of lockups was unbearable. Modern cards with fans are now very quiet when idle, and only sometimes noisy under load (which is irrelevent if you are gaming). The HIS IceQ range is superb in this respect.
PSU: Again, one with a 120mm fan. Corsair or Seasonic.
Hard drives: These can be remarkably irritating, and if you were to build a system on the lines of the above, may become the most annoying things in your case. Note, I did not say noisiest. You will be having 4 or 5 120mm fans going and a smaller one on the graphics card. These will make a noise even at 5 volts, but it will be a low, pleasant purr. The wrong hard drive can make a horrible, relatively discordant whine. You mention you have 2 on your Evesham. Suggest you review once you have built your new system, and if these are the cause of irritation, then swap to Samsung Spinpoints, or better still the WD AAK500s.
Fan Controller: The default fan speed for case fans is 12v. This is a veritable wind tunnel, even with 120mm fans. You'll need to reduce that to a whisper.
I have a Sunbeam Rheobus (hard to find, takes a bit of getting used to, but allows precise fan setting from stop to 12v). However, I think the new Zalman ZM MFC1 Plus will look fantastic in my Lian Li V1000+, and does 5v to 12v
http://www.overclockers.co.uk/showproduct.php?prodid=BB-001-ZA
Hope this helps.