The pre-installed versions (which the vendor of your PC paid less for than a full retail version) can't be moved. As far as Windows is concerned, your PC is your motherboard (for the most part, I'm not sure that's strictly true), so you could upgrade a lot of components but if it's on a new motherboard that's a new computer to it. If you have a full retail license you can reactivate it pretty easily on a new PC as you're allowed to move it.
If this leaves you high and dry, you can always use a free OS like Linux Ubuntu, but that won't be a great solution if you use Windows for gaming or need Windows-only software for work, but you'll have a working PC until you save some more money. Still, you can play some Windows games and use some Windows software on Linux systems using WINE, but if it's work-critical I wouldn't rely on it.