You can find it out using Linux:
sudo hexdump -s 56 -e '"MSDM key: "
Now, it is true that there are pre-activated keys for OEMs disks like HP, Dell, etc.. At least for Windows 7 it was like that. They have so called SLP Keys (System Locked Pre-Installation Key) and they are not the same as the one printed on your Windows 7 machine. SLP keys only work on a certain range of machines, but also have the advantage as working like generic OEM DVDs. I've had this case where a Windows Vista machine (Vista Key sticker) from Dell and I used the a Windows 7 Dell OEM disk, and
Given that from Windows 8 on the licenses are embedded in the firmware, this is over.
Personally, I think reinstalling from scratch is always the right option. With decrapifying you might miss something, and if you're routined, you have a reinstallation done rather quickly. If you stick with big brand machines, getting drivers is no Herculean task any more. Back in the day, oh, yes, I remember... Hard to find, need to use shady places, take drivers from different machines and try to see whether they work. Today, it's "go to manufacturer website", download what is *missing* and use what Windows gives you as default drivers for all the rest, with the notable exception of the graphics card.