The homepage will attempt to connect to inedo.com to download latest news, and it will also connect to the database to provide a summary of feeds (dashboard). However, if either of those operations times out, then you should get a prompt error.
Maybe, for some reason, the request isn't even being routed to ProGet. You can connect ProGet to a proxy like Fiddler (Admin > Proxy), and then attach to SQL Server to see if anything is timing out..