How can I add a Google account?

[lbandrew]

Can't add Google account

Attempting to solve "Contacts continuously updating" problem by deleting Google account in anticipation of adding it back.
When I then attempt to add my (existing) Google account, after entering data it asks for my name, and then...asks me whether I want to add a new or existing account. Whichever I pick, it returns to the same choice. Help!