Windows Update does not work after re-installing Windows!

The thing is that I have downloaded and then re-installed my Windows 8.1 OS, but then I can't seem to get the Windows Update working, and have tried many things. So is it possible to install Windows 10 on it to fix the problem, as I heard you can get a Windows 10 for free if you have Windows 8.1? And I only have the OEM Windows 8.1 key that came with the laptop.

Any help would be appreciated.

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