Yes, if COA sticker Product key has already been used for Clean Reinstall then it should be detected by a key finder program and work for reinstall. But if it's still the preinstalled Win7 installation, then it has a SLP key which itself can't be used to reinstall at all.
The factory SLP key must have it's entire onboard file backed up to reinstall using methods we are not allowed to support here.
The options then become to use whatever remains of the COA sticker to see if enough is there for MS Phone Activation to issue a new key to activate a Clean Reinstall. There are numerous reports they will do this if they can get enough off the sticker to verify it. I think they also ask for the Product ID which is a tracking code.
Or you can order the Recovery disks which self-activate.