Originally, I opened a bug report for PowerShell with Microsoft Connect (https://connect.microsoft.com/PowerShell/Feedback/Details/1821747) about this issue, but I have since learned it is with the PSReadline module included with Windows 10, and possibly previous versions.

On Windows 10, from the PowerShell console when using the command "Start-Process powershell -Credential (Get-Credential) -PassThru", while specifying credentials other than those of the current login (eg. CONTOSO\user is currently logged in, and specified CONTOSO\admin in the Get-Credential), the new PowerShell process becomes unresponsive to keyboard commands until either A) enter is pressed in the parent window, or B) the parent window is closed. In the case of A, when the enter key is pressed, the new window will begin typing whatever was put into the window. At that time, the parent window goes unresponsive until the reverse is done.

A workaround is done by issuing Remove-Module PSReadline prior to running Start-Process. However, you cannot reload the module or the issue resumes.