I ended up in an interesting licensing corner case thanks to an odd combination of circumstances: I had acquired Windows 7 Professional through the MSDN Academic Alliance programme (now known as DreamSpark), and had upgraded trouble-free to Windows 10, but was struggling to reactivate it after replacing a defective motherboard.
Entering my Win7 key in the Win10 activation tool reported that it couldn't be used with this edition of Windows 10 (despite having been automatically upgraded from Win7 Pro to Win10 Pro), and phoning Microsoft support confused the heck out of them, as they thought the key was for Win7 Enterprise Edition, presumably because MSDN-AA/DreamSpark keys are a weird halfway house between retail / Pro Edition licensing and wholesale / Enterprise Edition licensing. After much fruitless talk with various baffled support operatives, it was clear I'd need to figure this out by myself.
The root of the problem is, when upgrading from Windows 7 to Windows 10, the association with your original product key becomes quite weak. Rather the fact that Win7 attests your key is genuine is used to generate a Digital Entitlement for the particular hardware it's running on, and this must be re-done if the hardware breaks down. Typically it could be re-done by simply entering your Win7 key in the Win10 activation tool, but evidently the particular case of MSDN-AA editions is only patchily catered for, as the successfully generate an entitlement during upgrade but not on submitting the key to an already-installed Win10.
The "easy" solution is to reinstall Win7 from scratch, reinstall all your software, etc etc etc. Fortunately we can avoid that tedious route. Simply use Disk Management to shrink your existing C: partition, and create another by its side, of at least 50GB in size (fully updated win7 -> win10 is *big*). Then install Win7 in the new partition, leaving your original install untouched. Upgrade *that* Win7 to Win10 and the upgrade process will generate a new digital entitlement for your hardware. Then when you boot back to the original Win10 you'll find it picks up the entitlement and re-activates. Voila, you get to keep your existing install and avoid having to reinstall your software.
Hopefully eventually Microsoft will fix this such that any key that's good for generating an entitlement via upgrade is also good for generating one on an existing install; in the meantime I hope this can help Dreamspark/AA users avoid some tedious work.