Powershell: pass in multiline txt file values as an array in param statement

When you pass objects via the pipeline into a function, only one is passed into your function at a time - not the whole array. So you don't need the foreach loop, nor do you need to make $computers an array in the function.

Also, when you have a pipeline function, you should be making use of the begin,process and end keywords. Each denotes a script block - begin is a scriptblock that is executed once (when the pipeline is "set up"), process is the scriptblock to be executed for each object passed via the pipeline, and end is just like begin only it runs after the last item has passed through.

So minimally, your function should be this:

function Get-LocalAdministrators
{
    param(
    [Parameter(Mandatory=$True,Position=0,ValueFromPipeline=$True,ValueFromPipelineByPropertyName=$True)]
    [string]$computer
    )
process{
$ADMINS = get-wmiobject -computername $computername -query "select * from win32_groupuser where GroupComponent=""Win32_Group.Domain='$computername',Name='administrators'""" | % {$_.partcomponent}
# Do other stuff here
}
}

The MSDN documentation says (this is in get-help about_functions - there's more to it than this):

Piping Objects to Functions
Any function can take input from the pipeline. You can control how a function processes input from the pipeline using Begin, Process, and End keywords. The following sample syntax shows the three keywords:

      function <name> { 
          begin {<statement list>}
          process {<statement list>}
          end {<statement list>}
      }

  The Begin statement list runs one time only, at the beginning of 
  the function.  

  The Process statement list runs one time for each object in the pipeline.
  While the Process block is running, each pipeline object is assigned to 
  the $_ automatic variable, one pipeline object at a time. 

  After the function receives all the objects in the pipeline, the End 
  statement list runs one time. If no Begin, Process, or End keywords are 
  used, all the statements are treated like an End statement list.

Edit: After seeing the full code added by the OP, this works. Note that I have made the changes to your code as I describe above.

function Get-LocalAdministrators 
{
    param(
        [Parameter(Mandatory=$True,ValueFromPipeline=$True,ValueFromPipelineByPropertyName=$True)]
        [string]$computer
    )

    process{
        $ADMINS = get-wmiobject -computername $computer -query "select * from win32_groupuser where GroupComponent=""Win32_Group.Domain='$computer',Name='administrators'""" | % {$_.partcomponent}

        foreach ($ADMIN in $ADMINS) 
        {
            $admin = $admin.replace("\\$computername\root\cimv2:Win32_UserAccount.Domain=","") # trims the results for a user
            $admin = $admin.replace("\\$computername\root\cimv2:Win32_Group.Domain=","") # trims the results for a group
            $admin = $admin.replace('",Name="',"\")
            $admin = $admin.REPLACE("""","") # strips the last "

            $objOutput = New-Object PSObject -Property @{
                Machinename = $($computer)
                Fullname = ($admin)
                #DomainName  =$admin.split("\")[0]
                #UserName = $admin.split("\")[1]
            }

        $objReport+=@($objOutput)
        }

        $objReport
    }
}