You can always store the last userId of the user that successfully logged in. Then compare that Id with the current userId, if it's null then the user logged out, if not the same then it's a new user.
Edit:
User opens the app 1.a: User logs in => store some flag or userId (some info basically) 1.b: User does not log in => store some null flag or null userId
User closes app
Backgroundworker picks up the event, based on the flag or info you can figure out if the user logged in or logged out.
Depending on what you store, you can use AppSettings or IsolatedStorage among other options to store the flag.