The first error showing says "Blogger returned the following error: NotFound: Not Found
The WLW log file shows the following:
WindowsLiveWriter,1.27804,None,00031,27-May-2015 09:52:23.884,"WindowsLive.Writer.Extensibility.BlogClient.BlogClientAuthenticationException: Account Login Failed - Please check your user name and password.
NotFound - Not Found
at WindowsLive.Writer.BlogClient.Clients.GDataCredentials.EnsureLoggedIn(String username, String password, String service, Boolean showUi, String uri)",""
Not sure yet if this is an intentional change of the Blogger API or not. Hopefully Microsoft or Google fixes this issue soon.
Apparently this issue happens with other apps that are using the Blogger API too. Even Word 2016 Preview for Windows is not working with Blogger.
In the meantime a workaround that can be used is to create the post in Windows Live Writer and copy and paste to the Compose mode in Blogger, alternatively and sometimes the best option is to switch to Source in Windows Live Writer, select all, copy and paste to the HTML mode in Blogger. Note that this will not work if you normally upload images through Windows Live Writer. In this case you need to re-insert the images in Blogger. But if you have the images already online it is a decent workaround.