I have an HP 350 G1 Laptop running Windows 10 Pro, and recently have noticed that my Start Menu no longer opens when I click on the Windows icon in the taskbar.  The Windows Store icon doesn't work, either.  I've already tried entering the following commands in an administrator-level powershell window:

DISM /Online /Cleanup-Image /RestoreHealth
(The System File Checker said it didn't find anything)

sfc /scannow
(Didn't find anything)

Get-AppXPackage -AllUsers | Foreach {Add-AppxPackage -DisableDevelopmentMode -Register “$($_.InstallLocation)\AppXManifest.xml”}
(This just STALLS and never completes)

I would love some help to get my start menu back, if possible.  Thanks in advance for any help!Is this Windows 10 a legally installed Windows 10 or one that was acquired though a download other than Microsoft which is flawed?

Has this system been infected with a VIRUS that would attack this part of the OS to prevent removal of malware?left field approach...

install ClassicShell to at least get a Start Menu you can navigate with.
(it's about to reach end of SUPPORT but fully functional for a while yet)
you can then uninstall it and see if that process resurrects the Windows Start Menu.To answer the first question:  I'm not sure if it's a legitimate copy of Windows, as I purchased the laptop USED with Windows 10 pre-installed.  How would I check this?

It has not been infected with a virus any time recently, to my knowledge.

And I tried installing Classic Shell (which made the start menu work only while it was installed), but got the following errors during the installation: 

WARNING 1946.  Property 'System.AppUserModel.ID' for shortcut 'Start Menu Settings.lnk' could not be set.
Warning 1946.  Property 'System.AppUserModel.ExcludeFromShowInNe wInstall' for shortcut 'Start Screen.lnk' could not be set.

Any further help is much appreciated.I'd backup your data to a thumb drive. If your unable to do this in the current state that the system is in then get a live distro of Linux such as ubuntu or mint installation DVD or a bootable USB stick and boot to Linux. Then copy your important data to an external drive. When done with this then reinstall Windows 10 clean. You may or may not need a Windows 10 key to do this. The key might be on the BIOS in which none is needed.

Basically a reinstall is my suggestion at this point. If you dont have any important data to save them skip the Linux stuff and just install 10 clean.