What OS? I know exactly how to do it in Win2000. I have a real good guess about Win98. Have absolutely no idea (nor do I care to) about WinME.
Here's how for Win2000:
Get rid of the splash screen by adding " -nosplash" to the target url on the shortcut icon in: "C:\Documents and Settings\AllUsers\StartMenu\Programs\Startup"
right click "properties" and make it so:
"C:\ProgramFiles\ZoneLabs\ZoneAlarm\zonealarm.exe" -nopopup -nosplash
-in other words, add " -nosplash" (w/o the quotes) to the end of the path.
For Win98 I'd try going to the folder (I'm trying to remember here- I don't have a Win98 box close by and haven't used it for a year now) "C:\Windows\start\Programs\startup", right-click the Zone Alarm shortcut and choose properties and add the -nosplash to the target.