Google account issue
I cannot login with my Google account on El Capitan (OS X 10.11.1). It accepts my mail, password and 2FA verification code too (Google Authenticator).
After pressing the last Enter, the login window turns grey and nothing happens (no feedback, no spinning wheel etc.)
I've left it for an hour without doing anything else, but still the same.
The other account I am having issues with is iCloud. iCloud is signed in (my Clear to-do list which uses iCloud for sync is syncing as usual.
However, when I go to System Preferences > Internet Accounts > iCloud, opens for a few seconds than locks itself.
After entering my password it unlocks for a second, than "locks" again (the checkboxes become gray and unchangeable).
I'm also unable to change AirDrop to Contacts Only from Everybody. Previously AirDrop had the No One status and when I tried to change it asked for my iCloud password, but didn't change after entering.
Facebook and Twitter accounts are both logged in with no problem on my Mac. Furthermore, I can access both my Google and iCloud account through web browser.