Test when can remote connecting a machine while rebooting

Question

After restart a remote machine in PS, I need to test when it is available to connect in Remote Desktop.
I tired to use Test-Connection. But when it returns True, Remote Desktop still get error when connect. I tried the following and working ok (i.e. C:\RMC.RDP can connect ok) but with error. Any other way or without showing error?
Restart-Computer -ComputerName 172.16.0.3
Start-Sleep -Seconds 10
 While ((Get-Service -ComputerName 172.16.0.3 -DisplayName 'Remote Desktop Services').Status -ne 'Running' ) { Start-Sleep -Seconds 1 }
 C:\RMC.RDP
Get-Service : Cannot open Service Control Manager on computer '172.16.0.3'. This operation might require other privileges.
 At line:3 ((Get-Service -ComputerName 172.16.0.3 -DisplayName 'Remote Desktop Serv ...
 +         ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
     + CategoryInfo          : NotSpecified: (:) [Get-Service], InvalidOperationException
     + FullyQualifiedErrorId : System.InvalidOperationException,Microsoft.PowerShell.Commands.GetServiceCommand

Answer 1

Use script for checking RDP port response
like:
http://www.jonathanmedd.net/2011/12/testing-tcp-port-response-from-powershell.html