Try allowing 3rd party cookies in your browser. In Firefox, go to Tools -> Options -> Privacy, chose "Use custom settings for history" and check "Accept cookies from sites" and "Allow 3rd party cookies".
In Internet Explorer, right-click the IE icon, chose Properties, enter the "Privacy" tab and click "Sites". Type todoist.com and click "Allow".
If this doesn't help, please tell me which browser are you using and what exactly happens if you try to log in - do you see an error message?