Most special folders are accessible using special values, documented here: ShellSpecialFolderConstants enumeration

So, if you want to get the My Computer (a.k.a. "This PC") folder, you can do this:

$shell = new-object -com Shell.Application
$folder = $shell.NameSpace(17) # "ssfDRIVES" constant

And this will get you a Folder object.

There is another way wich uses the folder CLSID (a guid). It will allow you to get to any folder in what's called the shell namespace, even the ones that may not be defined in the enumeration above (3rd party shell namespace extensions for example). The syntax is this:

$shell = new-object -com Shell.Application
$folder = $shell.Namespace("shell:::{CLSID}")

In fact, this funny syntax combines the 'shell:' URI moniker with the shell namespace parsing syntax ::{CLSID}.

So for example to get the My Computer folder, you would do use the constant known as CLSID_MyComputer like this:

$shell = new-object -com Shell.Application
$folder = $shell.Namespace("shell:::{20D04FE0-3AEA-1069-A2D8-08002B30309D}")

This will also work:

$shell = new-object -com Shell.Application
$folder = $shell.Namespace("shell:MyComputerFolder") # direct shell: syntax

And it should bring you back the same object as in the previous call. They're all equivalent.

Once you have a Folder object, there is a last trick to get the associated verbs, because the Verbs() method is only defined on the FolderItem object. To get the FolderItem from the Folder (as a Folder is also an "item" in the namespace, so it has also a FolderItem facade), you can use the Self property, like this:

$shell = new-object -com Shell.Application
$folder = $shell.NameSpace("shell:::{20D04FE0-3AEA-1069-A2D8-08002B30309D}") # ssfDRIVES
$folder.Self.Verbs()

Ok, that was to get verbs for a FolderItem. To pin an item to start however, the "Pin to Start" verb invocation does not always work (for My Computer for example), or the verb isn't even available (for a standard folder for example). In general, it doesn't really work well for folders for some reason.

So, one solution for folders is to first create a shortcut file (.lnk) somewhere to that folder (including My Computer or other special locations), and pin that shortcut file to start. Note: the standard (non language localized) verb for Pin to Start is "PinToStartScreen", it's better to use that than to scan various verbs (all verbs have a canonical name). So the code would look like this to pin My Computer to start:

$wshell = new-object -com WScript.Shell
$shortcut = $wshell.CreateShortcut("c:\temp\mypc.lnk")
$shortcut.TargetPath = "shell:MyComputerFolder" # use the same syntax as described above
$shortcut.Save()

$shell = new-object -com Shell.Application
$folder = $shell.NameSpace("c:\temp")
$lnk = $folder.ParseName("mypc.lnk") # get the shortcut file
$lnk.InvokeVerb("PinToStartScreen") # invoke "Pin To Start" on the shortcut file

The fact is that's exactly what Windows does when we do "Pin to Start" on My Computer, it creates a shortcut in C:\Users\<my user>\AppData\Roaming\Microsoft\Windows\Start Menu\Programs