It depend how old you talk, for Pentium III and earlier the Powersupply is not compatible with P4 and even now AMD board need these recent powersupply. Check carefully before to do a move.
I have an old 486 running as a firewall and a Duron 1gig PC running as a server. They hum so loud I have to close the door between my office and the bedrooms because it bugs me so much when I try and go to sleep. surprisingly, my desktop machine which is a Lian-Li PC60 case with 7200rpm hard drive is really quiet. I definitely think a good case reduces the overall noise level of the computer.
I recently built a computer for someone: Antec 400W + Antec case (old 1040 model) with 4 Vantec Stealth case fans, and AMD Barton core xp2500+ with retail HSF. It's very quiet! I also use a APC power line conditioner with all my computers. I have very rare power outages, but have frequent dirty power and line sags. However you would not notice this unless you have one of these units. Before I got the line conditioner, I had occasional mysterious failures (power supply, slow monitor degredation). Cheaper UPS's will not filter noise or clean power. Edit: I have been using Maxtor 7200rpm drives recently (last year's 740dxl and the current Diamondmax plus 9 series with fluid bearings), and they are essentially inaudible.
If you own a Dell, Antec power supplies do not "fit" in a Dell without requiring "surgery" at the back of the case. You need to check out PC Power & Cooling. They are the only manufacturer of power supply units that will fit a Dell. I bought the "Silencer-400" just to make sure that I had sufficinet +12v rail and +3.3V rail power for my RAM and processor. I installed it in my new Dell 8300 in about 3 minutes. It is an expensive power supply, but extremely well made. You get what you pay for! http://www.pcpowercooling.com