How to iterate through XML in Powershell?

I have this XML document in a text file:

<?xml version="1.0"?>
<Objects>
<Object Type="System.Management.Automation.PSCustomObject">
<Property Name="DisplayName" Type="System.String">SQL Server (MSSQLSERVER)</Property>
<Property Name="ServiceState" Type="Microsoft.SqlServer.Management.Smo.Wmi.ServiceState">Running</Property>
</Object>
<Object Type="System.Management.Automation.PSCustomObject">
<Property Name="DisplayName" Type="System.String">SQL Server Agent (MSSQLSERVER)</Property>
<Property Name="ServiceState" Type="Microsoft.SqlServer.Management.Smo.Wmi.ServiceState">Stopped</Property>
</Object>
</Objects>

I want to iterate through each object and find the `DisplayName` and `ServiceState`. How would I do that? I've tried all kinds of combinations and am struggling to work it out.

I'm doing this to get the XML into a variable:

`[xml]$priorServiceStates = Get-Content $serviceStatePath;`

where `$serviceStatePath` is the xml file name shown above. I then thought I could do something like:

foreach ($obj in $priorServiceStates.Objects.Object)
{
if($obj.ServiceState -eq "Running")
{
$obj.DisplayName;
}
}

And in this example I would want a string outputted with `SQL Server (MSSQLSERVER)`

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.

<!-- language: sh -->

[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

<!-- language: sh -->

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

You can also do it without the [xml] cast. (Although xpath is a world unto itself.

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$xml = (select-xml -xpath / -path stack.xml).node
$xml.objects.object.property

Or just this, xpath is case sensitive. Both have the same output:

$xml = (select-xml -xpath /Objects/Object/Property -path stack.xml).node
$xml


Name Type #text
---- ---- -----
DisplayName System.String SQL Server (MSSQLSERVER)
ServiceState Microsoft.SqlServer.Management.Smo.Wmi.ServiceState Running
DisplayName System.String SQL Server Agent (MSSQLSERVER)
ServiceState Microsoft.SqlServer.Management.Smo.Wmi.ServiceState Stopped