Sweet, I had no idea Jack Bauer used PowerShell.
Anyway, to finish up the example, here's how you can loop on your 200 boxes:
$ServiceName = "My Service"
get-content computers.txt | % {
$remoteservice = gwmi win32_service -comp $_ | ? { $_.displayname -like $ServiceName }
$remoteservice.StartService()
}
Note the use of aliases:
% = foreach-object
gwmi = get-wmiobject
? = where-object (or its other alias "where")