I also use zone alarm and mine dosn't pop up anymore to tell me that it is running, but it is, as long as you have it in the taskbar then it is running so i wouldn't worry.
If it is running it will be here:
START--ALL PROGRAMS--ACCESSORIES--SYSTEM TOOLS--SYSTEM INFOMATION--SOFTWARE ENVIRONMENT--STARTUP PROGRAMS. and as long as Zone Labs Client is there then it is running on startup, so don't panic.