This is a problem that seems to have vexed a lot of people. Windows Live Writer worked just fine. Word 2013 will not register with Blogger nor allow you to install Windows Live Writer.
Here is how you get around that little issue. Download Windows Essentials. I know that it is not the best, but it works fine for me. I de-selected everything but Windows Live Writer and I am now able to post to my Blogger account.
I have read many postings starting with Word 2007 about this issue. Hopefully this will help a bit.