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I had exactly the same problem. Run Clean Up on Windows 10 and Start button became unresponsive. I was not able to open it at all. In the end I had to reinstall Windows 10! Waste of money in my opinion.
Some people recommended this method to get Start working again:
https://www.techmesto.com/fix-start-menu-broken-windows-10-technical-preview/
I did use it and was able to get into Start but tiles previews were broken, hence clean reinstall.
I hope support will look into it. Maybe Clean Up cleans something that is needed in Windows 10?