Nope. No sense. Give up on using that old drive as a windows 10 bootable drive. The motherboard OEM chip the OS license is tied to is in your old HP...just that one.
Your easiest (and cheapest) solution without breaking into your case is an external data transfer rig. You pop the HDD in, plug into computer via usb and transfer your data ... depending...again on the drive and models of computers and if you've attempted booting up with it in as a second drive before this still may lock the drive. It's not impossible, it just gets harder to get data off.
If your Win10 on the old HDD was an upgrade (the HP came with Win7 or something and you did the win10 upgrade) you should be able to then go to your MS account and assign the license to your newer computer without having to pay for it or pay for it again....maybe.
Mostly true however you can get the license much easier than going through any of that MS account nonsense. All you need is that rig you discussed with You are not allowed to view links.
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Login or make a 5 post minimum to see url tags. . I suggest getting an AIO adapter. Would be a IDE/SATA to USB converter(get a 3.0). They are cheap. Can get them for around 19.99 and cheaper. i suggest startech? id have to look at my adapters. I have about 4 of them from my previous IT jobs. All you need to do is get the enclosure or the adapter, connect the drive, i have a program that i use called Hirens which has a good 75+ portable programs on the .ISO. Recovery tools, virus removal tools, password recovery tools..etc. But if you can find that which only way is to torrent the file. very easy to find on google....but you just open it, find produkey or any of the other 4 programs. I like produkey. Can be found here for free
5 post minimum to see code tags! .. Once installed and hard drive is plugged in via adapter or directly into the motherboard, you can open produkey and tell it to search CD KEYS on external devices. It will then search your hard drive for the cd key. I have used this program for over 5 years and never had any issues grabbing keys. Even though yes the key is stored in the bios, it also gets logged in the registry where produkey can snag it.... Secondly the ONLY way you can plug that hard drive into a computer and boot it up without re-imaging..etc is to buy quite literally the EXACT same model of computer and swap the hard drives. This way all the HW associated with the machine will communicate with the registry keys implemented when the OS was first installed. That is going to be virtually impossible however....also a huge waste of money. I suggest following what You are not allowed to view links.
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Login or make a 5 post minimum to see url tags. said and the above information. Simply get an IDE/SATA enclosure or adapter and it treats the hard drive like an external hdd... Only issue you may come into is having to reset the permissions on the old drive which is extremely simple. PM me or message back here for further questions..etc Any HW or SW questions feel free to let me know. I was the mobility and technology supervisor and head technician at my last job so i have plenty of experience and certifications