4S: two step verification doesn't work

Hi,

My iPhones 4S doesn't accept two step verification.

I signed off all iCloud, iTunes, FaceTime, etc... Rebooted.

Now I turn iCloud on, and it asks for my iCloud password. Then it correctly switches to the two step screen and asks me whether I want to send an SMS to my iphone 6 or use my iPhone 6 (no sms) as a trusted device. Meaning it sees it and knows it has to use it.

The problem is that absolutely nothing happens when I click the NEXT button.

Then I tried to tell it to use the Recovery Key, but here again, once I hit NEXT, nothing happens.

Any idea? I'm stuck and can't use it to sync my contacts, notes, reminders, etc...

IPhone 4S, iOS 6.1.4 (no I won't update that OS, I need it)

Thanks for any help