I had the same problem.. what did the trick for me was going to my phone's "Settings", Apps, All, Google Play Store, Clear data.. Then I went to "Account & Sync", Google, Remove Account..
After doing everything(above).. I also went to "Security" (Setting--->General---->Security). Find "Phone Administrators" then click, "Android Device Manager"... Deactivate it!
Now, reboot your phone.. then go to "Security" again.. Reactivate Android Device Manager, go to Google Play Store and enter your email and password.. Done!
P.S. Make sure to set Require Authentication for Purchases to "Never" in your play store settings.
Play store is killing me! Authentication required but impossible!
