How do I get PowerShell 4 cmdlets such as Test-NetConnection to work on Windows 7?

You cannot. They rely on the underlying features of the newer OS (8.0 or 8.1) and cannot be ported back to Windows 7 . The alternative is to write your own functions / modules to replicate the new cmdlets using .NET framework methods.

For instance, the Get-FileHash cmdlet is a one-liner in PowerShell 4.0, but to replicate in 2.0 we have to use .NET.

PowerShell v4

Get-FileHash -Algorithm SHA1 "C:\Windows\explorer.exe"

PowerShell v2

$SHA1 = new-object -TypeName System.Security.Cryptography.SHA1CryptoServiceProvider
$file = [System.IO.File]::Open("C:\Windows\explorer.exe",[System.IO.Filemode]::Open, [System.IO.FileAccess]::Read)
[System.BitConverter]::ToString($SHA1.ComputeHash($file)) -replace "-",""
$file.Close()

At least Test-NetConnection can be ported back to Windows 7. Just copy folders NetTCPIP, DnsClient, and NetSecurity from the supported Windows machine with the same PowerShell version (Windows 8.1, Windows 10, etc). Folder - C:\Windows\System32\WindowsPowerShell\v1.0\Modules. Then Import-Module -Name C:\Windows\System32\WindowsPowerShell\v1.0\Modules\NetTCPIP -Verbose

Alternatively, you can import a module from a remote machine (say win2012):

$rsession = New-PSSession -ComputerName win2012
Import-Module NetTCPIP -PSSession $rsession

I have had the same problem on my Windows 7 x64 and both solutions worked for me as of PowerShell 5.1.

Adding to Anton Krouglov's answer. PowerShell modules are cross-platform compatible. So a module copied from Windows Server 2012 R2 x64 can be imported to Windows 7 x86, and even if you are running as standard user without rights to copy them to C:\Windows\System32\WindowsPowerShell\v1.0\Modules you can copy it to any local folder, and run.

Assuming you copied the NetTCPIP, DnsClient, and NetSecurity modules from a Windows Server 2012 or higher machine, and save them to a folder you can import them using

Get-ChildItem -Directory .\psmodules | foreach { Import-Module -Name $_.FullName -Verbose}
Test-NetConnection -InformationLevel "Detailed"