I have interrupted my holiday posts to just do a quick post on the problems that a lot of people seem to be having with logging in, and posting comments on Blogger.
My Blogger was doing the exact same thing about 3 weeks ago. It was not letting me leave comments on anyone's posts, and I kept on having to log in repeatedly just to do a blog post, and some days I couldn't even log in as myself! I looked into what could be the problem, did what it suggested by clearing my cache, browsing history etc. etc. and still no joy, until I read somewhere that older browsers are having trouble with the constantly updating websites (including Blogger) and to try downloading a new, fast browser such as Google Chrome.
Its free to download, and takes about 5 mins to install. (Its also super easy and safe by the way, no boffins required!) Quite simply the best thing I ever did - my computer is working MILES faster, all the pages open super fast and blogger works perfectly again.
Hope this helps a few of you out! :))