This is probably happening because your browser is blocking the pop-up window that Google uses to authenticate you. In this case you will need to temporarily disable pop-up blocking and then try the Google Drive button again. Note that once you have authenticated with Google, you can re-enable pop-up blocking. Attachments should still work - at least until Google wants to authenticate you again.
How to disable pop-up blocking:
- In Chrome: https://support.google.com/chrome/answer/95472
- In Firefox: https://support.mozilla.org/en-US/kb/pop-blocker-settings-exceptions-troubleshooting
- In Safari: https://discussions.apple.com/thread/6014396
- In Internet Explorer: http://www.wikihow.com/Turn-Off-the-Pop%E2%80%90Up-Blocker-in-Internet-Explorer