Only happened recently ... on my Samsung SG2 mobile phone. GT-I9100 running 4.1.2 no customization
When I go to Playstore I can't get any updates or new Apps it tells me my Google account is not logged in.
I go to accounts ... and my Google accounts says sync error against my @Googlemail account but the @gmail account is sync'ing fine.
(Neither are used for email)
When I go the Google App it has 'Sign in' button at top right ... when I click on it, the Login window showing gmail account opens but as soon as I click on password field it closes widow and goes back to main Google screen.
Same is I slect Sign in from left hand menu
Error seemed to coincide with the time I changed pwd on my youtube account.
Where do I need to go to update password?