How to iterate through XML in Powershell?

PowerShell has built-in XML and XPath functions. You can use the Select-Xml cmdlet with an XPath query to select nodes from XML object and then .Node.'#text' to access node value.

[xml]$xml = Get-Content $serviceStatePath
$nodes = Select-Xml "//Object[Property/@Name='ServiceState' and Property='Running']/Property[@Name='DisplayName']" $xml
$nodes | ForEach-Object {$_.Node.'#text'}

Or shorter

[xml]$xml = Get-Content $serviceStatePath
Select-Xml "//Object[Property/@Name='ServiceState' and Property='Running']/Property[@Name='DisplayName']" $xml |
  % {$_.Node.'#text'}