Anthony Nocentino has a quick Powershell script to see if ports are open on a machine:
Ever want to confirm that a port is accessible from one computer to another? There’s a PowerShell cmdlet for that, Test-NetConnection. With the -Port option, this cmdlet will do a quick TCP three-way handshake on the remote system to confirm that the service is available and reports back if it succeeded or not. Check out that last line of output TcpTestSucceeded: False. That indicates that this port is not accessible. You can see, however, that the system is reachable via ICMP (Ping), PingSuceeded: True so we know that the remote system is alive, just not listening on the port we want to access.
For when your security team won’t let you install nmap.