I know it looks a bit daunting, but I'm sure you already know that a lot of problems get solved through the process of elimination.

Your Dr.Watson log is called Drwtsn32.log, if you go to your system32 folder and execute Dr.Watson, you should get a report on any errors.

The .dll is attempting to place an icon in your notification area and will be listed in the bottom pane under explorer.exe in prcoexp, so we know that it is definitely one of them!
(This can be very useful in finding strings in some of those annoying virus pop-ups: Right-click the suspect .dll> go to properties> select the strings tab> check the memory button> and search for the text in the 'pop-up').

However it is obviously broken somewhere along the line, run a disk check on your next re-boot. Check your start-up programs and take note of them to see if something on the list isn't starting.

When you run the debugger, it is noticing the problem and just killing it, which is why the mystery icon disappeared.

If you need to check your settings for Dr.Watson, try the microsoft support site: Microsoft Windows XP - Using the Dr. Watson log file. Like you say, a bit daunting but I'm afraid you've started something!!!!

And this one helps you with interpreting the log file: Microsoft Corporation

Do any balloon tips come up when you hover over it?

You can also try a registry cleaner.

Regards

Martin