I got WLW working again after migrating to Blogger Beta. WLW didn't post at all and could not load the style template.
I got this tip by email from Joe Cheng at Microsoft that solved the problem. I initially posted about it to the msn Groups.
Find this registry key:
HKEY_CURRENT_USER\Software\Windows Live Writer\Weblogs\2e27accf-425c-4996-9c2d-a075aad9307a
Rewrite BlogId and PostApiUrl to use "beta.blogger.com" instead of "www.blogger.com" (leaving the rest of the URL the same). Then restart Writer and try again.