?
Unfortunately there's nothing for us to go on here; with the limited information we have here, everything appears to be fine (the 401 is to be expected when you have an authenticated feed).
Because you're using the unsupported VS2013 NuGet Plugin (which we cannot test with), and you upgraded from an a two-year old version of ProGet with a ton of changes between, we have no idea what is going on. We would need to know precisely which requests worked before (request/response), and precisely what it's doing now.
Otherwise, you should just consider rolling back to 3.8.6 until you can upgrade to a supported version of Visual Studio.