Does your PC have a product key sticker on it? As long as you have that key you can install the same Windows you had from a download. Windows are legal to download but it must be the same version as your own OS.
If you don't have that sticker, download Speccy and run it then click on Operating System and you'll see your product key. It's after serial no. Write it down for safekeeping.
Copy all the stuff you need to keep on disk because you'll have a lot less headache with doing a fresh install. I don't know how big your HDD but I'd partition it. If you have room to partition the HDD the way it is now I'd do it and move the stuff you need to keep there. Whatever happens to your boot drive does not affect the other partition (it's like another drive) so the data there is safe. Any program you've installed cannot be moved or saved, just data like your records, photos, videos, whatever.
EDIT: forgot to mention, after you reinstalled your OS you can activate it online and I think MS will do it. If not, explain to MS that you replaced the motherboard.