OK, so I've been tinkering with this one for a bit and got it working. At first, it looked like the script was running as expected, except that it would show an error message in the console whenever the reg query command didn't find the reg key that it was looking for. That in itself was not an issue, but after that I would have expected it to continue and run the if code block - instead it seemed to be skipping right on to processing the next object in the foreach-object queue from the pipeline. I am not sure what was going on there, but eventually I got the code to the point where it was evaluating everything correctly and trying to run the if code block. This time, I was getting the following error whenever the script hit an Out-Host statement: Out-Host : A positional parameter cannot be found that accepts argument mystringvar. Apparently there is something about using Out-Host that causes ForEach-Object to think that the processing code block is done. Anyway, I overcame this by switching to using Write-Output instead. Here's the final working code:

import-module bsonposh
add-pssnapin Quest.ActiveRoles.ADManagement

get-qadcomputer -sizelimit 0 -searchroot 'OU=MyComputers,DC=MyDomain,DC=lcl' | test-host -property name |ForEach-Object -process {
    $targnm = $_.name
    $tststr=(reg query "\\$targnm\HKLM\SOFTWARE\JavaSoft\Java Runtime Environment" /v Java6FamilyVersion)
    if(-not($tststr |select-string -simplematch '1.6.0_20'))
    {
        $mssg="Updating to JRE 6u20 on $targnm"
        Write-Output $mssg
        Out-File -filepath c:\install_jre_log.txt -inputobject $mssg -Append
        cmd /c \\myfileserver\apps\java\installjreremote.cmd $targnm
    }
    else
    {
        $mssg ="JRE 6u20 found on $targnm"
        Write-Output $mssg
        Out-File -filepath c:\install_jre_log.txt -inputobject $mssg -Append
    }
}

With what you've done, $listA has no element named "Item_One" so that expression is effectively NULL
It's an array, and if you want to get "A" out of $listA, you need to use $listA[0].Item_One and $ListA[0].Item_two
Without knowing more about this situation not quite sure what to suggest...
Do you really have so many items you need a CSV?
If not try a hash table

PS C:\temp> $listA = import-csv .\list.csv
PS C:\temp> $listA

Item_One                                Item_Two
--------                                --------
A                                       1
B                                       2
C                                       3


PS C:\temp> $listA.gettype()

IsPublic IsSerial Name                                     BaseType
-------- -------- ----                                     --------
True     True     Object[]                                 System.Array


PS C:\temp> $listA.Item_One

PS C:\temp> $listA[0].Item_One
A

PS C:\temp> switch ($Test)
>> {
>> $listA[0].Item_One {write-host $ListA[0].Item_two}
>> default {"Not found"}
>> }
>>
1

# Hash table example
$hash=@{"A"=1;"B"=2;"C"=3}
$hash.A
1

New after Nick's 7/9 comment:

I don't think the case/switch structure is a good fit for this case. This seems like it will do what you need.

$listA | foreach {
    if ($_.item_one -eq "A") {
        # do something
        write-host $_.item_two
    } elseif ($_.item_one -eq "B") {
        # do something different
        write-host $_.item_two
    } else {
        $found = $false
    }
}
if ($found -eq $false) {
    write-host "default"
}

Depending on your needs, the IF clause could also be begin like this

if ($_.item_one -match "A|B|C") {