This problem was there prior to the last update of the Windows 10. The problem was that the Windows desktop manager was not letting the menu to open. The reason being the customization menu options often create such problem. This has been addressed in many tech channels and forums. And many people have managed to fix this in multiple ways. So there is no one specific fix for the start menu options.
Fix 1: I suggest you to restart the PC in troubleshooting mode. Press Windows button and L key. And this will log out from your session. Now go to the Power icon and select restart. Here you can choose troubleshoot option. And from this option you can point to "Reset". You should also choose "Keep my files". So there is no loss of personal data.
This small fix is going to temporary fix the start menu. Do note that updating the Windows 10 will fix any such issues that have caused since the release.
Hope this works in your case.