Hello Fulufhelo,
Thank you for reaching out about adding your desktop computer to your Microsoft 365 account I understand how frustrating it can be when the system does not recognize the serial number especially after purchasing a new device for your son. You’ve taken the right step by trying to link the device and it’s important that everything works smoothly so your son can enjoy the new desktop without issues.
The serial number is not typically required to add a device to your Microsoft account. Instead you need to sign in to the desktop using the same Microsoft account credentials. Once signed in the device will automatically appear under your account at account.microsoft.com/devices . If the desktop is not showing make sure Windows is activated and connected to the internet. You can check activation under Settings select Update & Security select Activation. If the issue persists try updating Windows and restarting the device.
Could you confirm if you have already signed in to the desktop with your Microsoft account and checked the activation status?
I hope this answer is helpful if you have further questions feel free to reply back
Regards,
Marcelo