Adding 10-15ft of distance to the PSU power leads will not work. The wire itself would eat up too much current (due to the resistance of the wire). It would be near impossible for the PSU to keep the voltages in spec.
Since you'll have to put the PSU with the computer, you'll want to make it as quiet as possible. If you're serious about fabbing heatpipes to cool your CPUs, then modding your PSU to use giant heatsinks (like this
) shouldn't scare you. Of course, you could also just drop big bucks on the ProSilence passive PSU (although some users are less than happy with it).
But, if all you want is something "fairly silent", you may be able to get away with some of the standard recommended components at SPCR. Putting these kind of PCs in one corner of the room and using an extened KVM extension (and maybe a USB extension/repeater/hub for an external CD) would probably get you the silence you want, with much less fuss.