Two of mon three 2012R2 machines exhibited this behavior dernier April. They would hang at Checking for updates... forever.
I jamais learned exactly what caused le problem, mais I did get it resolved by doing le following:
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Arrêtez le Windows Update service.
net stop wuauserv
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Supprimez le Windows Update cache directory C:\Windows\SoftwareDistribution.
Remove-Item -Recurse -Force C:\Windows\SoftwareDistribution
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Redémarrez le computer. (On one machine it requis plusieurs restarts to actually get everything deleted depuis this directory, so keep trying si necessary.)
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Run Windows Update manually again. It will fail almost instantly et offer to run a diagnostic tool. Download the tool et allow it to run.
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The tool will find et fix certains problems. At this point, run Windows Update manually again. Windows Update worked fine at this point.