Fix #126: GitHub Authentication is b0rked.

On 24 April, GitHub made a change making the User Agent mandatory in API
requests. This change adds that header to our one API request, and
includes a small amount of refactoring to accommodate the change more
easily (switching from WebRequest to WebClient).
Merge pull request #150 from alastairs/issues/126

Fix #126: GitHub Authentication is b0rked.