<p>I'm working on a simple ASP.Net page (handler, actually) where I check the value of the LOGON_USER server variable.  This works using Visual Studio's built-in web server and it works in other sites deployed to the live intranet site.  But it doesn't work on the IIS instance on my local XP machine.  How can I fix it, or what's going on if I can't?</p>

What authentication do you have enabled in IIS?  Anonmyous, Basic, Digest, Integrated Windows?  Sounds to me like anonymous access is enabled/allowed, and nothing else.  This would means that LOGON_USER is not populated.
When you access your local IIS, trying using
http://127.0.0.1
in particular if you use IE.  IE will recognize "localhost" as being in your local trusted zone and will automatically pass your XP login credentials through when Integrated Windows auth is enabled.