Finding Product Key on a Preinstalled Win 8.1 Laptop

So I have this Lenovo laptop with a preinstalled Windows 8.1 Pro 64 bit, and somehow I managed to mess with it to the point that I can't boot to normal or safe mode, and refresh or reset the system. I have tried different methods to fix this (renaming software to software.001, trying to boot to safe mode, etc) yet no success. One of my friends told me that the OS is corrupted, so I want to do a clean reinstallation of Windows 8.1 but given a preinstalled machine, I don't have the CD with me. I haven't downloaded an installation media from microsoft website yet because I realized I don't know the product key. I have searched through my laptop's box and case with no result. With that done said, can I know my windows product key while I cannot even boot? (I'm stuck in windows recovery environment)

P.S. I dont really know much about computer so please forgive me if I sometimes sound dumb
 
I have backed up all the important documents so I don't mind losing all my files.

Also, do I really need a product key if I want to reinstall by using an USB installation media?
 
Update: I have made an installation media, and have tried to reinstall windows. Problem is, the windows won't detect the product key asociated with the UEFI and it asks me to input the key again
 
Did I download a wrong version of windows? I'm pretty sure it is build 6.3.9600 (written on the command prompt). Is it windows 8.1 Pro?
 
Using KeyFinder is likely to be too late now that the OS has be reinstalled - - you needed it BEFORE you lost the existing system.
 
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