Of course you can reinstall Windows. Rather than wiping your current drive I would be inclined to replace it, and take the chance to upgrade it to an SSD. Both conventional disks and SSDs are cheap as chips nowadays and if your current disk is mechanical an SSD would be a significant upgrade.
The disk doesn't need to be totally corrupt to prevent Windows from booting or installing. Just a problem with the first few sectors would cause that.
You should not need a product key to reinstall -
https://answers.microsoft.com/en-us/windows/forum/al...
--------------------------------------------------------------
People have a tendency to blame politicians when things don’t work, but as I always tell people, you get the politicians you deserve
Barack Obama