Gordon,
Have you made any changes to the web.config in the Proget website? Also, can you go through some of the IIS settings as well? Version of IIS, authentication modes that are enabled. Also, take a look at the providers for 'Windows Authentication' and what does that list look like?
I did a little digging and found a somewhat similar situation on a completely different product (SiteFinity). In that forum discussion there is talk about changes in the web.config causing the issue. Thus why I'm asking about what your proget installation web.config looks like.
Please note, I do not work for ProGet, I'm a fellow customer offering assistance.