But the fact of the matter comes down to this. Taking the hard drive out of a machine, especially if it is pre-built, is going against the EULA (End User License Agreement). the reason being as they install OEM versions. Those OEM versions are tied to the mother board until the death of that mother board. So taking out a pre-built machines hard drive and putting it into a new system requires you to purchase a new license of Windows. If you have a retail copy, you must first format the drive and reinstall it on the new machine. This is also per the EULA of Windows. In order to transfer a retail license you must first remove it from the existing machine and install it on the new machine in order to complete the transfer properly.
So anyway you look at it, this is not the way to do it, even if it does work. It violates the EULA and basically makes your install a pirated install per the EULA. Even though it still says it is a valid install and updates, you broke the EULA which you agreed to when you first booted up Windows and checked the box saying you agreed to those terms. So all aspects aside with if it can be done or not is voided by the EULA. That is your agreement with Microsoft that you will use the software as they have stated. Since you checked the box and agreed, you have to abide by their rules.
I know it stinks, but it is the terms of use of the software.