Technically yes, new unused OEM key will work from the computer's standpoint. Answer already given above that switching keys is built-into windows.
But legally, OEM systembuilder keys are not supposed to be sold or used by the DIY individual homebuilder either. But by far this is the least enforced thing, and I think you are in the clear.
Before you buy another key, If you want to try your luck at social engineering, you can call the microsoft hotline that pops up with your OLD key and say you upgraded your computer and installing windows and it's saying you need a key; and reports say *sometimes* the person answering the phone just gives you a new key.
The rule is supposed to be locked to the Mobo, and approved only if previous mobo was damaged or broken (not a working upgrade).
But the reality is Microsoft reps sometimes are lenient.
If you feel this is fraudulent, well in some sense it is microsoft rep that "approved" your usage and gave you the new key, so it is somewhat a grey area.
As long as you are not lying, I would say this is similar to a restaurant giving you a free dessert (and not because you misled or lied to them) or an airline upgrading your seat, or calling your cable company and them giving you a discount.
For all the straight-and-narrow folks, I challenge you to call your cable company and demand they charge you full price.
Again, I'll say you don't need to lie. But it is only *sometimes* they give you a new key.