The PowerShell -and conditional operator

Try like this:

if($user_sam -ne $NULL -and $user_case -ne $NULL)

Empty variables are $null and then different from "" ([string]::empty).

You can simplify it to

if ($user_sam -and $user_case) {
  ...
}

because empty strings coerce to $false (and so does $null, for that matter).

Another option:

if( ![string]::IsNullOrEmpty($user_sam) -and ![string]::IsNullOrEmpty($user_case) )
{
   ...
}

The code that you have shown will do what you want iff those properties equal "" when they are not filled in. If they equal $null when not filled in for example, then they will not equal "". Here is an example to prove the point that what you have will work for "":

$foo = 1
$bar = 1
$foo -eq 1 -and $bar -eq 1
True
$foo -eq 1 -and $bar -eq 2
False