I didn't think this was allowed, so I looked it up. Here's what Microsoft has to say on the matter:
So yes, that is possible. Just once though, and only on retail versions since the OEM ones are locked to specific hardware. Also if they did the windows 8 upgrade, the key will still be in use, so again it won't work.
If you really want a free operating system, there are plenty out there. Ubuntu would probably be the easiest for someone who isn't very into computers, though I don't like how bloated the newer versions feel. Personally, I like debian, but you need to be comfortable using a terminal to really be able to get full use out of it.