KMS license can be installed via an illegitimate way from malware.
Good news is, you have OEM license and you have verified that it was embedded in the motherboard? If so, the focus is to get Home reinstalled on the computer, activation will take care of itself automatically, with one exception. If the computer was originally Windows 7 or 8, then the OEM license cannot be used to activate Windows 11 Home, you will need a separate Win 11 license in this case.
To reinstall Home edition, it will require a clean install. There's no supported way to go from Pro to Home.
So, make sure you backup your files first.
The following steps should be done on a working Windows computer:
Download the Windows Media Creation Tool from Microsoft's official website. https://www.microsoft.com/software-download/windows11 click on the "download now" button under "Create Windows 11 Installation Media"
Run the tool and select "Create installation media for another PC."
Choose "USB flash drive" as the media to use for the installation and select "Next."
Connect a USB flash drive with at least 8 GB of free space to your computer.
Select the USB flash drive you want to use, and then select "Next."
The tool will then download the required files and create the installation media.
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Now these steps will be done on your problematic computer:
Go to the computer's BIOS boot menu to have it boot from the USB drive.
Follow the on-screen instructions to install Windows 11, making sure to choose "Custom install" and select the option to delete all existing partitions.
Once the installation is complete, you'll have a clean installation of Windows 11 on your computer.