hard drive - Move HDD to another laptop, can't change Windows 7 product key

One of my clients returned to me a Dell Latitude laptop that runs Windows 7 Pro with an OEM product key (bad motherboard).

Now, I have a laptop that is the same model (it is already set up with Windows and all, but that doesn't matter), so I took the HDD from the old machine and put it in the one I have so that all the user's data and settings will be there and I don't have to move any files.

My problem is that now I need to change the product key to match the COA on the new machine. But Windows says it is activated (with the COA from the old machine) and does not provide me with the "Change Product Key" link that is usually in the System Properties panel.

I am afraid that, given time, Windows will realize that it's OEM key doesn't match the motherboard it is in and then starts complaining that it isn't genuine.

Funny thing is that the Product ID is correct! That is, if I use NirSoft's Produkey application, the Product ID it reports matches the one in the System Information. System Information doesn't tell me the Product Key, however, and doesn't offer me the link so I can change it to match the one on the COA sticker for that machine.

How can I change the product key - or do I need to? Or can I mix and match product keys for Dell Latitude e5520 laptops?

[update]

I just discovered that the product key of the old laptop does not match it's own OEM sticker. That's weird. It's like Windows makes up it's own product key or something.

[update]

I confirm that the Product Key that was used by the old computer is the same as the one used on the new computer.

Also, I have a third identical machine and it shares the exact same Windows PID as the other two in question, and neither does this machine show the "Change Product Key" link; and it is factory.

Answer

Ah, in the end, I don't have any problem since both machines are the same model and both are OEM. Apparently, Windows activated itself automatically. If there were a discrepancy with the keys, the "Change Product Key" link would be there.

Here is an answer from TechNet:

The OEM ( Dell in your case) uses the same key ( may be different
between machine models, may not) on all the machines, which is tied to
information in the BIOS of those machine to meet the activation
requirement.

The key on the side of the machine does not need to be used unless
there is an issue with the OEM activation process( the bios loses the

signature, the key inside the OS is accidently removed or corrupted).
The key on the side requires the machine to be activated via the
Microsoft Activation servers.

And another fellow says:

if you do want to change your product key

run command prompt as admin.

In the CMD window, type:
`slmgr.vbs -ipk ` (without the <>)
To activate windows after changing the key, type: slmgr.vbs -ato 

But i wouldn't suggest it, we have machines here from dell and they
all have the same product key as well. You can tell cause in the
product key it will have OEM in there, which is what dell uses for the

preactivated keys

So, that commandline is like this:

slmgr.vbs -ipk ABCDE-12345-FGHIJ-67890-KLMNO

If something changes, I'll post back here. But as it stands, I was able to move the HDD from one machine to the other and Windows still works and is still "genuine" and still "activated". I wish I had checked the product key before I loaded the HDD in the new machine.

So, in the end, I conclude that since the two machines are the same model and have the same OEM Product ID, that the Product Keys are interchangeable.