Thanks for the tip. I ran several varieties of malware searches and didn't find anything. There's nothing suspicious in my msconfig listings. I've tried removing and reinstalling both products several times. What I find consistently is this. I can successfully remove and reinstall both, in any order without incident. After I restart the computer, for any reason, the systray icon for Systemworks disappears. The desktop and start menu shortcuts for both programs stop working. The systray icon for Internet Security remains visible and double-clicking on it launches Internet Security.
This laptop previously had both NIS and NSW installed and working. I did a complete wipe and Windows reinstall. Since then, I haven't been able to install either NIS or NSW without the above problems.
<<Edit: Changed post subject to match the problem>>