You do not say what results/errors your code generated.
$Service = 'BeyondLogic RmtExec Server' <- I would recommend that you use the short name (name of the key for the service) in HKEY_LOCAL_MACHINE\SYSTEM\CurrentControlSet\Services
ServiceRun ($Computer, "BeyondLogic RmtExec Server", 1) <- this is not the UDF name. It is fADSIServiceRun.
If you provide more details, I could provide a better answer.
