There are numerous international agencies that regulate electronic emissions of electronic devices. Most use Class A and Class B designations.
Class A devices are devices that are designed for use strictly in a business or industrial environment. Class B devices must meet more stingent emissions tests to make them suitable for a residential environment.
All this is a long winded way of saying that my bet is that the noisy computer was probably not designed to meet Class B standards. The only way to bring into standards would be to replace all components that don't meet those standards. I would start with the power supply as it is probably the "noisiest" electronic component. The next step would be to replace the case with one that has proper shielding.
If you are interested, the following URL provides a list of the different regulatory agencies, the areas of the world they govern, and the pertinent regulations:
http://www.elotouch.com/support/agencies.asp
(remove any embedded spaces from the URL)
Hope this helps.