Hi,
Relocating the switch shouldnt be hard, if you are talking about the front panel push button switch. That's because that is all that it is, a momentary contact push button switch. You press in, it makes contact, you release it, it breaks the contact. It could not be simpler.
So all you really need to do is take off the front cover of the computer and splice into the push button switch and wire a second one in parallel to that one. If you dont want to do that, then just find the mother board connection for the on/off switch. It's usually on an IDE type header and it's only two pins so you could unplug that and plug your own connector into the motherboard and run your own wires and add your own switch. I would not say you could run a mile of wire this way, you it should be ok for say 5 feet or maybe 10 feet.
The above assumes that your computer can turn off with the same button. Mine does, when you hold it in for something like 4 seconds it turns the thing off. Pressing it again a few seconds later will start the computer up again.
If you need to extend the power supply switch itself, you may have to use a different kind of switch. They usually use a DPST rocker switch but any DPST switch that can handle the power can be used. It's a little more dangerous to do this kind of mod however so you should be careful and only if you have ever wired 120vac circuits up before or know how to do so. You also need to remove the cover of the power supply so you had better be careful and get it back on right.