<p>I am creating a standalone asp.net page that needs to be embedded into a sharepoint site using the Page Viewer Web Part.  The asp.net page is published to the same server on a different port, giving me the URL to embed.</p>

<p>The requirement is that after a user is authenticated using Sharepoint authentication, they navigate to a page containing the asp.net web part for more options.  </p>

<p>What I need to do from this asp.net page is query Sharepoint for the currently authenticated username, then display this on the page from the asp.net code.  </p>

<p>This all works fine when I debug the application from VS, but when published and displayed though Sharepoint, I always get NULL as the user.  </p>

<p>Any suggestions on the best way to get this to work would be much appreciated.</p>

When it works in debug, is that being used in SharePoint?
Your page and the Sharepoint site might as well be on different servers as far as authentication is concerned -- in order to get the information over you might need to pass it via the QueryString from the webpart if you can -- or you might need to make your own webpart to do this (just put an IFRAME in the part with the src set to your page with the QueryString passing the username).
It does seem that this would be a security issue if you use the name for anything though -- if you are just displaying it, then it's probably fine.
If you actually need to be authenticated, you might need to add authentication into the web.config of the site hosting your standalone page.
edit: I think you'd have better luck putting your page on the same port and server as SharePoint.