Hello

Did you let the original GApps from the Rom, or did you flash another GApps? I ask, because we never had this problem before...
You can try following:
1) Go to Settings, Apps, right down click on menu - show system processing. In the list search for Google Play Services and Google Services Framework, Google Playstore, Gmail - go inside the Apps to Memory and delete data and Cache in those Apps.
Do this with every Google App (Google Account Manager, Google Backup Transport...)
2) Go to Advanced Settings to date and time and set a wrong time (example: instead of today 6: pm set yesterday 6

m)
3) Be sure, you have
not activated in K-Settings, More settings, Block Ad (this blocks Google Services) - for blocking Ads use AdAway!
4) Delete your Google Account one time more
5) Reboot your phone
6) Go to Advanced Settings, Time and date and correct the time to the right one.
7) Set up your Google Account - now everything should work