I had exactly the same , I error checked my main C: drive which is a Samsung SSD, Windows reported that it had found some errors and it needed to be rebooted to correct them. I rebooted the PC and the check disk did it's repairs and it booted back in to Windows. I noticed straight away that the start menu had stopped working and when I opened Windows Explorer or did anything within it (like right click properties) or any settings windows like control panel it would take for ever. Opening programs like Internet Explorer work fine.
I have tried System Restoring to before I did the drive repair and sfc /scannow and Dism/Online/Cleanup-Image /RestoreHealth but I still had the problem. The SFC found errors and corrected them but still no Start Menu.
I do a full True image back up weekly so I rolled back one week and stupidly did another check drive for errors and exactly the same happened, I also tried an in place upgrade (
Repair Install Windows 10 with an In-place Upgrade) but as soon as the system booted after the upgrade the start menu did not work the same as before the upgrade.
What I did in the end is roll back 2 weeks and I have not done a check drive for errors and it's been ok ever since for 2 weeks, fingers crossed.
I did find a few posts about opening up a new user account, I did this and on the new account I had a start menu and the system opearated as normal. So if it's going to be a major reinstall how about opening a new user account, transferring all your files in to it and see if that works.
I'm sure MS will sort this out soon as there are many posts about it.
Cheers
Tony