Tony, I had the same question at one time and found building the box myself was the best solution. Asking for something out-of-the-box might be like searching for the Holy Grail!
I'm using a great CoolerMaster case*, which is double-walled and uses a metal mesh instead of plastic for the bay covers. The power supply uses shielded cables and has been the quietest RFI pc I've owned. For what it's worth, here's what's in the box I have. I don't know if this has contributed to low noise, but here it is: Intel motherboard (DQ35JO) & Core 2 Duo 3.0 CPU ATI x1650 PCIE (512MB) 2 sticks of 1GB Corsair XMS2 (DDR2) 2 250GB Seagate Barracudas (RAID0) Plextor DVD-RW Memory card reader in the floppy slot (All this for less than a Dell, dude.) The board has on-board sound, but pretty decent, offering a S/N ratio of around 95 dB. Better than a SoundBlaster Live. Great for digital modes. Using an LCD monitor is also a great idea. I recommend taking an AM radio to your local LCD reseller and scan across the ones they have on display. I got funny looks when doing so, but it's a good opportunity to educate the salesperson! I found that CTL and Viewsonic have some quiet models. PLEASE let us know the make and model if you find a RF quiet one. It might save us some work later. I also added ferrites and toroids in the case to where ever I thought they should go, including all fans. Be sure to wrap a couple around the cables from the front USB & audio jacks. These might not be necessary, but I didn't want to troubleshoot the RF later. My hand-held AM radio gets zero buzz from the tower, but wave it in front of a CRT (even one of my LCDs) and it lights up! *The case model is here: http://www.coolermaster.com/products/product.php?act=detail&id=2908 Whichever enclosure you get, stay away from those silly Plexiglas-type clear side panels! I also have the system grounded and the rig and PC on the same power outlet. I have the rig right under the PC, with a tin plate to further shield it. An overall picture of my setup, including my favorite 'accessory' can be seen (for now) via the link below. Hope that helps some! 73. Frank K2NCC http://evokefrank.googlepages.com