Which Powershell Function could check whether a certain port is in LISTENING state on localhost?

If you're using PowerShell v3.0+ on Windows 8/Server 2012 or later, then instead of trying to connect to the port to determine the state, you can simply use Get-NetTCPConnection:

Get-NetTCPConnection -State Listen

To me this is more accurate as it's reading the status of the port on the computer. Using a connection to test can make it seem like it's not "LISTENING" when it is, if a firewall or alike gets in the way or something.

First create and store the connection:

$connection = (New-Object Net.Sockets.TcpClient)
$connection.Connect("127.0.0.1",10389)

Then check if it's connected

if ($connection.Connected) {
    "We're connected"
    }

Or as suggested by Colyn1337

Try {
    $connection = (New-Object Net.Sockets.TcpClient)
    $connection.Connect("127.0.0.1",10389)
    "Connected"
    }
Catch {
    "Can't Connect"
    }