I have not had any success in resolving this issue on my laptop. But lo and behold, the system works fine (normally) on my desktop.
This is very frustrating. I have been pulling my hair out trying to figure out what the differences could be in configuration.
Both machines run Windows 7 Home Premium; both use Firefox 39.0 as browsers. Both use the same Norton Internet Security software.
Have uninstalled and reinstalled Windows Live Writer several times, and toggled various settings on google/blogger security settings.
Still get 'method not allowed' whenever I hit publish.
Maddening.