This is a simple PowerShell port scanner that you can run against one or more hosts and check one or more ports to see if they are open.

function Test-Port{
<#
.SYNOPSIS
    Tests port on computer.

.DESCRIPTION
    Tests port on computer.

.PARAMETER computer
    Name of server to test the port connection on.

.PARAMETER port
    Port to test

.PARAMETER tcp
    Use tcp port

.PARAMETER udp
    Use udp port

.PARAMETER UDPTimeOut
    Sets a timeout for UDP port query. (In milliseconds, Default is 1000)

.PARAMETER TCPTimeOut
    Sets a timeout for TCP port query. (In milliseconds, Default is 1000)

.NOTES
    Name: Test-Port.ps1
    Author: Boe Prox
    DateCreated: 18Aug2010
    List of Ports: http://www.iana.org/assignments/port-numbers

    To Do:
        Add capability to run background jobs for each host to shorten the time to scan.
.LINK
    https://boeprox.wordpress.org

.EXAMPLE
    Test-Port -computer 'server' -port 80
    Checks port 80 on server 'server' to see if it is listening

.EXAMPLE
    'server' | Test-Port -port 80
    Checks port 80 on server 'server' to see if it is listening

.EXAMPLE
    Test-Port -computer @("server1","server2") -port 80
    Checks port 80 on server1 and server2 to see if it is listening

.EXAMPLE
    Test-Port -comp dc1 -port 17 -udp -UDPtimeout 10000

    Server   : dc1
    Port     : 17
    TypePort : UDP
    Open     : True
    Notes    : "My spelling is Wobbly.  It's good spelling but it Wobbles, and the letters
            get in the wrong places." A. A. Milne (1882-1958)

    Description
    -----------
    Queries port 17 (qotd) on the UDP port and returns whether port is open or not

.EXAMPLE
    @("server1","server2") | Test-Port -port 80
    Checks port 80 on server1 and server2 to see if it is listening

.EXAMPLE
    (Get-Content hosts.txt) | Test-Port -port 80
    Checks port 80 on servers in host file to see if it is listening

.EXAMPLE
    Test-Port -computer (Get-Content hosts.txt) -port 80
    Checks port 80 on servers in host file to see if it is listening

.EXAMPLE
    Test-Port -computer (Get-Content hosts.txt) -port @(1..59)
    Checks a range of ports from 1-59 on all servers in the hosts.txt file

#>
[cmdletbinding(
    DefaultParameterSetName = '',
    ConfirmImpact = 'low'
)]
    Param(
        [Parameter(
            Mandatory = $True,
            Position = 0,
            ParameterSetName = '',
            ValueFromPipeline = $True)]
            [array]$computer,
        [Parameter(
            Position = 1,
            Mandatory = $True,
            ParameterSetName = '')]
            [array]$port,
        [Parameter(
            Mandatory = $False,
            ParameterSetName = '')]
            [int]$TCPtimeout=1000,
        [Parameter(
            Mandatory = $False,
            ParameterSetName = '')]
            [int]$UDPtimeout=1000,
        [Parameter(
            Mandatory = $False,
            ParameterSetName = '')]
            [switch]$TCP,
        [Parameter(
            Mandatory = $False,
            ParameterSetName = '')]
            [switch]$UDP
        )
    Begin {
        If (!$tcp -AND !$udp) {$tcp = $True}
        #Typically you never do this, but in this case I felt it was for the benefit of the function
        #as any errors will be noted in the output of the report
        $ErrorActionPreference = "SilentlyContinue"
        $report = @()
    }
    Process {
        ForEach ($c in $computer) {
            ForEach ($p in $port) {
                If ($tcp) {
                    #Create temporary holder
                    $temp = "" | Select Server, Port, TypePort, Open, Notes
                    #Create object for connecting to port on computer
                    $tcpobject = new-Object system.Net.Sockets.TcpClient
                    #Connect to remote machine's port
                    $connect = $tcpobject.BeginConnect($c,$p,$null,$null)
                    #Configure a timeout before quitting
                    $wait = $connect.AsyncWaitHandle.WaitOne($TCPtimeout,$false)
                    #If timeout
                    If(!$wait) {
                        #Close connection
                        $tcpobject.Close()
                        Write-Verbose "Connection Timeout"
                        #Build report
                        $temp.Server = $c
                        $temp.Port = $p
                        $temp.TypePort = "TCP"
                        $temp.Open = $False
                        $temp.Notes = "Connection to Port Timed Out"
                    } Else {
                        $error.Clear()
                        $tcpobject.EndConnect($connect) | out-Null
                        #If error
                        If($error[0]){
                            #Begin making error more readable in report
                            [string]$string = ($error[0].exception).message
                            $message = (($string.split(":")[1]).replace('"',"")).TrimStart()
                            $failed = $true
                        }
                        #Close connection
                        $tcpobject.Close()
                        #If unable to query port to due failure
                        If($failed){
                            #Build report
                            $temp.Server = $c
                            $temp.Port = $p
                            $temp.TypePort = "TCP"
                            $temp.Open = $False
                            $temp.Notes = "$message"
                        } Else{
                            #Build report
                            $temp.Server = $c
                            $temp.Port = $p
                            $temp.TypePort = "TCP"
                            $temp.Open = $True
                            $temp.Notes = ""
                        }
                    }
                    #Reset failed value
                    $failed = $Null
                    #Merge temp array with report
                    $report += $temp
                }
                If ($udp) {
                    #Create temporary holder
                    $temp = "" | Select Server, Port, TypePort, Open, Notes
                    #Create object for connecting to port on computer
                    $udpobject = new-Object system.Net.Sockets.Udpclient
                    #Set a timeout on receiving message
                    $udpobject.client.ReceiveTimeout = $UDPTimeout
                    #Connect to remote machine's port
                    Write-Verbose "Making UDP connection to remote server"
                    $udpobject.Connect("$c",$p)
                    #Sends a message to the host to which you have connected.
                    Write-Verbose "Sending message to remote host"
                    $a = new-object system.text.asciiencoding
                    $byte = $a.GetBytes("$(Get-Date)")
                    [void]$udpobject.Send($byte,$byte.length)
                    #IPEndPoint object will allow us to read datagrams sent from any source.
                    Write-Verbose "Creating remote endpoint"
                    $remoteendpoint = New-Object system.net.ipendpoint([system.net.ipaddress]::Any,0)
                    Try {
                        #Blocks until a message returns on this socket from a remote host.
                        Write-Verbose "Waiting for message return"
                        $receivebytes = $udpobject.Receive([ref]$remoteendpoint)
                        [string]$returndata = $a.GetString($receivebytes)
                        If ($returndata) {
                           Write-Verbose "Connection Successful"
                            #Build report
                            $temp.Server = $c
                            $temp.Port = $p
                            $temp.TypePort = "UDP"
                            $temp.Open = $True
                            $temp.Notes = $returndata
                            $udpobject.close()
                        }
                    } Catch {
                        If ($Error[0].ToString() -match "\bRespond after a period of time\b") {
                            #Close connection
                            $udpobject.Close()
                            #Make sure that the host is online and not a false positive that it is open
                            If (Test-Connection -comp $c -count 1 -quiet) {
                                Write-Verbose "Connection Open"
                                #Build report
                                $temp.Server = $c
                                $temp.Port = $p
                                $temp.TypePort = "UDP"
                                $temp.Open = $True
                                $temp.Notes = ""
                            } Else {
                                <#
                                It is possible that the host is not online or that the host is online,
                                but ICMP is blocked by a firewall and this port is actually open.
                                #>
                                Write-Verbose "Host maybe unavailable"
                                #Build report
                                $temp.Server = $c
                                $temp.Port = $p
                                $temp.TypePort = "UDP"
                                $temp.Open = $False
                                $temp.Notes = "Unable to verify if port is open or if host is unavailable."
                            }
                        } ElseIf ($Error[0].ToString() -match "forcibly closed by the remote host" ) {
                            #Close connection
                            $udpobject.Close()
                            Write-Verbose "Connection Timeout"
                            #Build report
                            $temp.Server = $c
                            $temp.Port = $p
                            $temp.TypePort = "UDP"
                            $temp.Open = $False
                            $temp.Notes = "Connection to Port Timed Out"
                        } Else {
                            $udpobject.close()
                        }
                    }
                    #Merge temp array with report
                    $report += $temp
                }
            }
        }
    }
    End {
        #Generate Report
        $report
    }
}