After a recent upgrade of my Windows XP, with SpeedStartup, three programs open up a window on startup. Is there any way to stop them from opening the window, leaving them loaded?  They are Network Magic, Norton 360, and Skype.

I do not understand what you are asking.
What do you mean by, "open up a window"?
How are these programs being run?  through SpeedStartup?

Originally, when I had Norton 360, Skype and Network Magic, they would load and place an icon on the tray. I had made some adjustments, and had to re-enter them into the SpeedStartup lineup. Now, on booting, the programs open by displaying their windows, which I have to close to clear the screen.

   Have you run the Scan in Speed Startup and removed their startup items?  That is what I would suggest doing.  Your upgrade may have reentered them in startup.  If so, you need to remove them again using Speed Startup.