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What you mentioned here, this is a common issue for a particular version of Windows 10. MS has a fix (KB article) to solve this issue. This is here: https://support.microsoft.com/en-us/help/3050653/the-user-name-and-password-box-might-not-appear-on-the-sign-in-screen-in-windows-10-technical-preview
Else you can reboot the system, and press ctrl + alt+ del to regain the logon/ password box. It can be done several times to achieve the same. Or you can insert Windows 10 setup/boot disk and try to repair startup of Windows 10 follow by Repair your computer link.