The key is the only part of the operating system that needs to be saved...
Anything else is are your personal files that have nothing to do with the os.
For one key viewer:(many more out in the web)
http://www.nirsoft.net/utils/product_cd_key_viewer.html
Find your key,
Write down your key ON PAPER - stick it with some tape UNDER your computer.
You wont have to remember where it is.
You will have it if your phone goes to crap, or gets hacked.
If you could rely on your pc for it - you wouldn't be copying it on to paper.
ALT:
Make an install cd and write the key on it.
... ISO you can grab anywhere, if whatever Microsoft page you are stuck on wont give it to you. People who are out in foreign countries often grab them from local torrents because they don't want to wait extensive download times from MS servers. Its completely legal. The legality part is about the key, the install you can get anywhere, obviously don't get it from too shady places :)
In any event you should have the key onhand as any misstep with your install and loss of key puts you through having to recover that key via microsoft, which can get tedious.