Well, based on the statement you just made you covered it yourself: if you were attempting to and then successfully did use a Product Key to install and activate Windows on a given computer, you can't use that same key again on any other machine because it's tied to the activation of just one machine - one key, one license, that's how it works. The basic gist of it (and I repeat this a lot):
The Product Key printed on the COA sticker is of no particular use in most any situation - it's a placeholder, nothing more because the license is the sticker itself, not what's printed on it.
With OEM hardware like an HP machine, or a Dell, or a Gateway or whatever manufacturer, the Product Key that's printed on the COA sticker is irrelevant in the big picture - it doesn't matter, at all, to any degree whatsoever. It's there for show and nothing else really because that's not what makes things legitimate - the sticker itself is the license.
Having said that, again the issue is that OEM installations of Windows on OEM hardware don't require a Product Key during the installation of the OS at all anyway - if you have one of those HP machines, and you have a branded HP Windows installation disc and you have the COA sticker on the hardware that matches the edition of Windows i.e. you have a Windows 7 Home Premium COA stick on a laptop and you have an HP Windows 7 Home Premium installation DVD then during the installation from that DVD you won't be asked for a Product Key.
Why? Because there are three variables at work when dealing with an OEM machine:
1) the BIOS or the UEFI of the OEM machine will have information embedded in it that corresponds to the edition of Windows that it's licensed for (the COA sticker is there just for show, to be honest) aka a digital certificate that says "Ok, from the factory this machine had <whatever edition of Windows> installed on it and here's the software licensing information aka the SLIC table so the installer can verify this..."
Next comes the OEM installation media aka "an HP Windows installation DVD" that will have the remaining two variables that are related:
2) it will have an OEM Royalty Product Key which is used for the activation that's done during the installation process from OEM branded media - the Royalty Product Key is not and never will be the same as the one that's printed on the COA sticker because as already stated the one on the sticker really is pretty much meaningless overall
3) it will have a digital licensing certificate known as an xrm-ms file (that's the actual extension, .xrm-ms) which is a digitally encrypted certificate hashed to the specific OEM only, so an HP xrm-ms cert is not going to work for a Dell machine, etc
When you install Windows using a branded OEM disc (HP disc for an HP, Dell for Dell, etc) those three variables get checked against one another during the installation and when it all matches, you get an installation of Windows on the OEM hardware that is activated as soon as the installation is completed - you don't even have to be connected to the Internet or Microsoft for that to happen. The activation happens because the formula is "complete" with the three variables needed.
I know it can seem really complex but it's not - for me I've had to learn all this over the years, decades actually, so to me it's truly "old hat" and stuff I can describe and over-explain too easily like I seem to have done so far in this thread.
Suffice to say I think you folks understand this better than you did, or at least I hope you do.
There's only one instance where the Product Key on a COA sticker is of any actual use and that's if you have the System Builder OEM installation DVD for Windows (whichever version). With that, the Product Key on the COA sticker can be used to install Windows because the key when entered defines the edition of Windows being installed.
But that's enough from me, I'm babbling on now and I think I've covered this quite enough, probably way too much but I'm ok with that: I'd rather provide too much than have people come back at me with "You didn't tell me that..."
