Good thought, kdyer. I'll consider adding that.
Here's the final code with the MessageBox implemented:
Code:
Break On
Dim $SO,$Pause
$SO=SetOption('Explicit','On')
$SO=SetOption('NoVarsInStrings','On')
$SO=SetOption('WrapAtEOL','On')
 
Dim $ArrayComputers, $sComputer, $Process, $Processes, $List, $Item
$ArrayComputers = 'OFF-FRONTDESK','OFF-TSINGERY','OFF-JHUFF','OFF-SGONZALEZ','OFF-HOYT','OFF-SBERGER','OFF-RLOCKWOOD'
$Processes = 'School.exe','SMinder.exe','SMAdmin.exe','SMReport.exe','SMBill.exe','Admission.exe'
For Each $sComputer in $ArrayComputers
  If $sComputer
    If Ping($sComputer) Goto "EnumDisplay"
	
		:EnumDisplay
       For Each $Process in $Processes
         If $Process
            $List = EnumProcess($Process,,$sComputer)
            If $List
              MessageBox($sComputer + " was pinged and is running " + $Process + " with a PID of" + $List + ".","SMChecks",0)
            EndIf
         EndIf
       Next
    EndIf
  EndIf
Next


Kind of nasty with the goto statement but it gets the job done.