Nuget Package Manager 3.4.4 for Visual Studio 2015 does not work with our local NuGet server. Apparently, they broke something compared to version 3.3.0, some redirect or whatever. New client sends requests that the server does not understand and returns error 404. I installed NuGet 3.5.0, but it did not help either. So, I had to downgrade back to 3.3.0, which has its own problems.
Apparently, backward compatibility is not the strong side of NuGet, which is weird for a package manager…