I'm not entirely certain I know which window you are talking about opening & closing but I'll take a shot at this anyway.
I know of three windows: the Main VI Window, the Window belonging to the Target process which you are trying to start and the System Exec window that appears during the startup of the Target process.
On the example I provided, as it was provided, when it is run on my Windows XP system, I briefly see the System Exec window open and then close as the Target process is being started. If I modify the example so that the (internal) Run Minimized input is set to TRUE then I never do see the System Exec window briefly open and then close. The Target process just pops up running.
In the case of the example, the Target process is the windows system calculator and Run Minimized will have no effect on that Target process because the calculator pops its own window up and the Run Minimized option is actually directed at the windows RUN command rather than the calculator process. Additional windows calls could probably be made to minimize the calculator window after it was up and running but that's another subject.
On my system the System Exec window never does stay open for this example program. If the example program behaves the same way on your system but then later the System Exec window does stay open when you substitute a different Target process then that has something to do with the new Target process and its interaction with the RUN command and not anything LabVIEW is doing.
This topic provides a way of killing off a process on a windows system.
Perhaps that might help you to close a few unwanted windows?
