Microsoft uses a combination of hardware IDs (specific components on the system with unique serial numbers) and an actual license key to ensure a device is licensed. This is how sometimes you appear to do a fresh reinstall but the drive activates without a key. You can still pull a traditional license key and it can usually be used to activate 2 distinct devices, but the actual licensing terms are pretty ambiguous in that they say you can only do one device but actually allow 2 or more. Sometimes replacing too many components and activating windows again results in the activation check.
Yeah this specific issue sucks to troubleshoot because sometimes the only way to be 100% sure it is the CPU is to have a exact same model CPU and throw it in and see if it works… I would isolate ram too, see if 1 stick works, etc.