Not really an answer, but to long for a comment:
Your code shows how you send the credentials to the server. So my previous comment still fits. You can't just pass variables to a new page. When a page is loaded this is like a application restart. You can pass values in the URL you redirect to, as cookies if both pages are loaded from the same domain or you can just reload them from the server where you stored them previously. To know that the new page is was requested by the same user you have to use some session handling (like the previously mentioned session cookie). This has nothing to do with Dart or Polymer this is more about how the web works.