Windows 10 activation error after OS re-installation

One of my clients has Windows 10 PC with a failing hard drive (corrupted boot sector makes the file system unrecognizable). I tried to repair the boot sector unsuccessfully. I run chkdsk to repair the drive, and it becomes readable and it scans as fine, but on reboot, it reverts to unreadable.

I manage to backup all of his data securely and moved to another hard drive that I am planning to reinstall Win10 onto. However, he doesn’t have an activation key (it’s a second-hand PC). There is a recovery partition that is not corrupted.

If I reinstall windows (from a bootable recovery USB that I made from another PC), will I be able to use the existing installation, or the recovery partition, to authenticate Windows? I’m trying to figure out to what lengths I go to try to repair the boot sector on this damaged drive. Since I was planning to move to the new HD anyways, or if I can just abandon the original drive after using it to authenticate Win10.

Thanks

Hey,
I suggest the link below.
http://answers.microsoft.com/en-us/insider/wiki/insider_wintp-insider_install/how-to-activate-and-resolve-common-product-key/33f31475-93b3-4d1c-812f-4b21fbd807a7