Windows 10 Failed Activation - New Computer

I'm not sure if this is the right place to ask a question like this... here it goes anyway.

I recently purchased a new laptop from Dell with Windows 10 pre-installed. No problem. I thought that I had a free version of Windows 10 Education through my university but it appears not. I entered a product code for Education which did not work (it's still not clear to me how that failed... it came from Microsoft.Azure...)

Fine, no problem, I'll just go back to 10 Home. I found my product key from the terminal command and I enter it in. Failed.

Windows troubleshooting fails, and entering the key yields this error: 0xc004f050.

I hear many people saying all I can do is re-install Windows. I sincerely hope not as I spent quite a bit of time setting up this environment. Likewise, I find it hard to understand how that is necessary when all I did was enter a bad code. It's not like I made any software changes...

This may be a bit of a low-brow question, but hopefully someone can help out.

Thanks.

If you have activated your new computer with this Windows 10 Home product key before you install Windows 10 Education, there is no need to install the Windows 10 home product key again. As Windows will reserve the activation information on Microsoft Server side. So just go to This PC, right click it and choose "Properties" to check for Windows Edition version.

If it shows as Windows is not activated, please check the system version occurred whether Windows 10 Home or others. Or we could run "slui.exe 4" to have a phone call activation.