Is there any update with this? Something that Toodledo does in their programming for their mobile site prevents connections from working sometimes. It's not a cookie issue, this is the only site that I have trouble with. The regular website and iOS app work fine, it's only these desktop tools.
I'm also experiencing the same problem. OSX 10.9.2 and on first install nothing happens when you click on "Sign In" button ... close the app and reopen it and it says "Connecting..." and then you get "Could not load data from Toodledo.com"
I can connect without any issues to the web site on the same MacBook. And my iPhone and iPad can connect using the iOS app. Everything is on the same WiFi network.
I've just tried both versions of the app (from your site and also the AppStore) and I see the login/password page now. Unfortunately after entering my userid & password when I press "Sign In" nothing happens :-(