This scipt will get the list of computers you want to check, ping for availability, then produce a text file with your results.  It also produces a file of computers that where not available.  Disclosure:  This is my 1st script. 

function PING {
 PROCESS {
  $results = gwmi -query "SELECT StatusCode FROM Win32_PingStatus WHERE Address = '$_'"
  foreach ($result in $results) {
   if ($result.StatusCode -eq 0) {
    write $_ >> c:\Ping.txt
    }
   else
    {
     write $_ >> c:\NoPing.txt
    }
    break
   }
  }
 }

New-Item -type file c:\Ping.txt -Force
New-Item -type file c:\NoPing.txt -Force

$Ping = gc c:\computers.txt | PING
 
 
function BIOS {
 
 Process {
  foreach ($Asset in $Assets) {
   $name = gwmi win32_computersystem -computerName $_
   $Bios = gwmi win32_Bios -computerName $_
   }
   $a = $name.name
   $b = $name.model
   $c = $Bios.SMBIOSBIOSVersion
   $computer = ("$a,$b,$c") >> c:\BiosVersion.txt
    }
  }
New-Item -type file c:\BiosVersion.txt -Force
$Result = gc C:\Ping.txt | BIOS

OK - went to Sapien/Don Jones class.  Let's see if the re-write is better 

 function TestPing([string]$address) {
 PROCESS {
  $address = $_
  foreach ($computer in $computers) {
   $ping = Get-WmiObject -query "SELECT * FROM Win32_PingStatus WHERE Address = '$address'"
   
   if ($Ping.StatusCode -eq 0) {
   
    $Currentuser = Get-WmiObject Win32_ComputerSystem -computerName $_
    $Bios = Get-WmiObject win32_Bios -computerName $_
    $User = Get-WmiObject win32_computersystem -computerName $_
    $name = Get-WmiObject win32_computersystem -computerName $_
    
    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode
    $obj | Add-Member NoteProperty ComputerName $name.name
    $obj | Add-Member NoteProperty ComputerModel $name.model
    $obj | Add-Member NoteProperty CurrentUser $Currentuser.Username
    $obj | Add-Member NoteProperty BiosVersion $Bios.SMBIOSBIOSVersion
    $obj | Add-Member NoteProperty BiosSerialNumber $Bios.SerialNumber    
    Write-Output $obj
   }
   Else {
    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode
    $obj | Add-Member NoteProperty ComputerName $name.name
    Write-Output $obj
   }
  }
 }
}
$results = Get-Content c:\logs\computers.txt | TestPing
$results | Export-Csv c:\logs\BIOSInfo.csv

#To make the script more flexible, I would add parameters for the input file and output file
 param
 (
     $ComputersToTest = 'c:\users\(your username here)\documents\computers.txt',
    $output = 'c:\users\(your username here)\documents\BIOSInfo.csv'
 )
 
 function TestPing([string]$address) {
 PROCESS {
  $address = $_
  
  #The foreach ($computer in $computers is not needed).  $computer was never assigned anywhere.
  
   $ping = Get-WmiObject -query "SELECT * FROM Win32_PingStatus WHERE Address = '$address'"
   
   if ($Ping.StatusCode -eq 0) {
   
    $Currentuser = Get-WmiObject Win32_ComputerSystem -computerName $_
    $Bios = Get-WmiObject win32_Bios -computerName $_
    $User = Get-WmiObject win32_computersystem -computerName $_
    $name = Get-WmiObject win32_computersystem -computerName $_
    
    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode
    $obj | Add-Member NoteProperty ComputerName $name.name
    $obj | Add-Member NoteProperty ComputerModel $name.model
    $obj | Add-Member NoteProperty CurrentUser $Currentuser.Username
    $obj | Add-Member NoteProperty BiosVersion $Bios.SMBIOSBIOSVersion
    $obj | Add-Member NoteProperty BiosSerialNumber $Bios.SerialNumber    
    Write-Output $obj
   }
   else {
    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode
    $obj | Add-Member NoteProperty ComputerName $name.name
    Write-Output $obj
   }
  }
 }

#The last two lines could be consolidated into 
Get-Content -ReadCount 1 $ComputersToTest | TestPing | Export-Csv $output
#and specifying a ReadCount of 1 means it will pass each line down the pipeline rather than waiting
#to read the whole file before passing each line down the pipeline.  Could be faster if you have a long
#list of computers

Great to see the use of custom objects however one thing... Your executing the same query four times.  The beauty of Custom objects is you can go out get all your data, and then return exactly what you need.  Having said that try changing...

$Currentuser = Get-WmiObject Win32_ComputerSystem -computerName $_
    $Bios = Get-WmiObject win32_Bios -computerName $_
    $User = Get-WmiObject win32_computersystem -computerName $_
    $name = Get-WmiObject win32_computersystem -computerName $_
    
    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode
    $obj | Add-Member NoteProperty ComputerName $name.name
    $obj | Add-Member NoteProperty ComputerModel $name.model
    $obj | Add-Member NoteProperty CurrentUser $Currentuser.Username
    $obj | Add-Member NoteProperty BiosVersion $Bios.SMBIOSBIOSVersion
    $obj | Add-Member NoteProperty BiosSerialNumber $Bios.SerialNumber    
    Write-Output $obj

TO:

$ComputerSystem = Get-WmiObject Win32_ComputerSystem -computerName $_
    $Bios = Get-WmiObject win32_Bios -computerName $_

    $obj = New-Object PSObject
    $obj | Add-Member NoteProperty PingStatus $ping.statuscode


    $obj | Add-Member NoteProperty ComputerName $ComputerSystem.name
    $obj | Add-Member NoteProperty ComputerModel $ComputerSystem.model
    $obj | Add-Member NoteProperty CurrentUser $ComputerSystem.Username
    $obj | Add-Member NoteProperty BiosVersion $Bios.SMBIOSBIOSVersion
    $obj | Add-Member NoteProperty BiosSerialNumber $Bios.SerialNumber    
    Write-Output $obj

Not trying to nit-pick but, you will see a significant performance increase as you scale up!