If you have "Recovery DVD" supplied by the PC manufacture then you do not need a product key. Just re-install Windows.
If this is not what you are asking for then
here are some utilities, all of which will display your product keys:
Note: For OEM product key sticker locations see the end of this post.
Also if you have an OEM version of Windows pre-installed by the manufacture
then the product key displayed by a "Product Key Finder" can not be used to
re-install Windows.
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Retrieve your Windows 7 / 8/ 8.1 product key before or after you upgrade to Windows 10
Download: http://www.softpedia.com/get/System/System-Info/ShowKeyPlus.shtml
Review: http://www.intowindows.com/how-to-recover-windows-product-key-from-windows-old-folder/
Windows 10 Embedded Product Key Tool
The NeoSmart Technologies Embedded Product Key Tool. Designed for users of Windows 7, Windows 8, and Windows 10,
This embedded product key tool will retrieve and display the Windows setup product key embedded in the BIOS or EFI, allowing you to store it for safe-keeping or use it to reinstall Windows with an official Windows setup image.
The embedded product key is not wiped when you format or reinstall, or when you replace your hard disk;
it’s stored in the NVRAM of the BIOS/EFI on the motherboard itself.
https://neosmart.net/blog/2014/windows-10-embedded-product-key-tool/#more-3188
Belarc Advisor: http://www.belarc.com/free_download.html
(It does a good job of providing a wealth of information.)
Will display your Windows XP, Vista, Windows 7 and Windows 8 product key.
However may not detect an Office key, so try one of the other two listed below for Office Keys.)
Also: http://www.nirsoft.net/utils/product_cd_key_viewer.html
and: http://www.magicaljellybean.com/keyfinder.shtml
(Jellybean has the ability to retrieve product keys from unbootable Windows installations)
Faqs: https://www.magicaljellybean.com/keyfinder-faq/
Paid (Free demo available): Recover Keys: http://recover-keys.com/
"quickly analyzes your system for over 3000+ software programs
and produces a list of software activation keys"
=========== Where is my product key sticker =========================
Check the side of your PC case or bottom of the laptop for the key code.
(or inside the laptop battery case, you may need to remove the battery)
If there is a sticker with the code it will most likely not
match what is displayed by the utilities mentioned above as OEMs such as
Dell use an internal key code when they build your PC.
The key code on the sticker is for use with your Windows CD
(that hopefully came with your PC) if you ever need to reinstall Windows.
J W Stuart: https://www.pagestart.com