I decided to restore an image backup I had made just before switching to Windows 10. Then I downloaded Win10 from the pending updates (the system image took me back to Windows 7 just before I decided to upgrade) and the Start button problem went away. My personal files were not affected but I had to download the software I had added since then all again. Fortunately there were very few softwares I addded during that period.
In case anyone here is still having the problem, I may have found a solution. There are some posts about Dropbox possibly causing this. I had Dropbox installed in 1 of my profiles, so I uninstalled it, rebooted the computer & boom - no more critical error!
Don't know if this is a common link, but an easy solution to try.
Kind of interesting that dropbox is the cause as I do have dropbox too but what is causing it to only happen randomly as mines always happens a month after the last Windows 10 install. Perhaps dropbox can fix the problem too.
That would be nice if Dropbox fixed the problem. But for now, I'm glad to know what the problem is & have been able to fix it. I have dropbox on another computer as well & have not had this problem, but will be removing it from that computer as well (just in case).
The problem is I wonder how does one reproduce the problem for dropbox to even believe us. Maybe it's the version of dropbox that's installed? Dropbox 3.10.11 is what I have but that's from a auto-update I think as it shows a install date 2 days ago. I've installed dropbox for years and Program and Features will usually update the date to the last Windows 10 install which for me was October 24, 2015.
I just experienced the critical error/start menu issue on my Win10 install. I uninstalled dropbox and problem went away.
Observations;
When problem happens, task icons all load in the ^ menu vs. on the bottom right task bar. Cortana is broken, the notifications are broken and I am sure other things are broken. Seems like a corrupted profile. So, I concur on DropBox being part of the problem. Maybe dropbox can't load and then halts processing of loading the profile for the user. I am going to reload dropbox now and see if all is well.
What version was the dropbox that was uninstalled? I used to have the problem when dropbox 3.10 was installed and basically, I would need to do Windows in-place upgrade installs to repair the problem with build 10240 about every 28 days since August 11, 2015 and then the same amount of time after each in-place repair upgrade until I heard about the dropbox issue. So I uninstalled dropbox 3.10 and installed dropbox 3.11 in November and the problem has never returned on both 10240 and now I'm at 10586.36.
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