Thanks for getting back to me. Since your Office was pre-installed and you've already tried both the recovery tool and the license transfer option without success, the next step is to get in touch with a Microsoft support agent who can manually reset the license for your current hardware.
You can do this by going to https://support.microsoft.com/contactus, selecting “Microsoft 365 and Office,” then choosing “Technical Support” and “I can’t activate Office.” From there, click “Chat with a support agent” or “Call me back.” When prompted, just let them know that your Office 2024 Home and Student was pre-installed, and after a motherboard replacement and system reinstall, it now says the license is already used.
They’ll be able to verify your account and help transfer the license to your current setup. Let me know once you’ve had a chance to try that, or if you’d like me to walk you through the support form step-by-step.
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