When you click "Sign In" in the Store menu nothing happens. When you click the "Sign In" link in the store nothing happens. You haven't got FruitMenu or APE (Application Enhancer) installed so the official line:
http://support.apple.com/kb/TS3638
is no good to you at all. You've checked your account in iTunes to make sure everything's ok, you've signed out, signed in, logged out, logged in, restarted your mac and it hasn't helped. Hey, you've even bravely deleted stuff from ~/Library/Caches/ and removed .plists from ~/Library/Preferences/ and you still can't get a sign in on the app store.
Take a deep breath.
You have Little Snitch installed. You've gotten annoyed with storeagent constantly phoning home and you've blocked it completely. Go to the Little Snitch Configuration. Unblock storeagent.
Launch the app store, click "Sign In" and smile.