Maybe try enrolling on your phone instead of your desktop. I had a mighty battle with AppleTV recently trying to sign up for Apple TV (which I would guess uses the same payment system). I suspect the root issue for me was that my copy of Windows boots off a non-encrypted drive, and was being considered as a non-secure connection. (I'm dual-booting with an older version of Ubuntu).

Anyway. Paying on my phone worked the first time.