How can I find out what program keeps popping up in my taskbar and disappearing before I can click on it?

I'll start with the relatively obvious: check what's starting when you login. A previous article, What's all this stuff running after I boot Windows? covers several of the techniques you can use to examine your system and determine all of the different programs and utilities that start each time you boot or login. You'll probably be surprised at how much there is. With that alone you may be able to say "oh yeah, that's it" when you stumble on something you didn't realize was starting on login.

If simply examining your startup doesn't give you any clues, my next approach would be to use SysInternals Process Explorer. Process Explorer actually highlights processes as they start and stop ... leaving them highlighted on its display for a few seconds after they exit. The only "trick" here is that you'll need to add Process Explorer to your start-up programs, and hopefully in a position that it starts and is running before the event you're attempting to diagnose.

I picked up this next trick from reading Fred Langa's LangaList: grab your video camera or digital camera and take a video of the screen as the item pops up and disappears. Now, watch that video in slow motion, or even frame by frame. You may now be able to discern the text in the task bar button, and use that as a clue to return to some of the techniques above. (This technique works great for error messages and blue screens that occasionally fly by as well.)

Finally, on Windows XP, 2000 and NT, you can also enable something called "process tracking". This will create a log of all processes that come and go on your machine. You may get overwhelmed with data, but the answer is almost certainly in the results. This article - How can I track what programs come and go on my machine? has the details.