When you start your Windows 10 system, you can sign in and the system gets part way to the desktop when the error message appears: “Critical Error: Start Menu and Cortana failed to load. We will try to fix at the next start up.”
To resolve the issue, leave the system on and as is. Right click with the mouse on an open area of the desktop. Click New and then Folder to create a new folder. Open the folder and then click File. Click on Open Command Prompt, then click Open Command Prompt as Administrator.
At the dos window, type at the blinking cursor sfc /scannow. The scan will run for awhile and may or may not report any issues. After the scan is complete, (it may take 15 to 20 minutes), restart the system. The problem should be resolved.
Finally, create a restore point immediately after successfully restarting the computer without the error. Right click the This PC icon, or click on Start and then do so. Click Properties and then in the upper left corner click Advanced System Settings. Click the System Protection tab. Then click to Create a restore point. Name it and click Create. Done. If the original error message comes back you now have another method to resolve it, (and other issues as well).