The hard drive that you are referring to is it the drive with the OS on it or just a storage drive ? If the OS is on it then you may hjave a diffacult time getting it authorized because the Windows insallation is tied to the motherboard. So with a new motherboard and cpu Windows will become unactivated and require a reactivation. I f it's just a data drive then if your using the same OS then you should have no problems.
If you could specify which type of drive you are transfereing then we can discuss it further.