Thanks both for your input.
I'm not quite sure I understand how to do these. In order to run sinv32.exe on the client, will I need to set up the whole package, program, and advertisement to get this to work?
And the same for the cliutils /start "software inventory agent" suggestion? I'm still a bit on the elementary side of SMS!
I do want to make sure I understand how these suggestions are supposed to work. But here is the good news--my software inventory is working now! Don't know what happened, but yesterday it all started working and updating!