Same here. The Continue button does nothing, and there is no error message shown, and there is no way for me to continue. Possibly related, there is some text that says "Terms and Conditions", and I guess that there should be a checkbox there but there is none.

I had a special character (+) in my email address. Once I went to Account Settings and changed my email address to one that only contained a-z 0-9 . and @, the checkout page worked for me. It did however pull an old Billing address from a previous year, which was weird, but it worked anyway.

I got help from their service group and it was also because I had a "+" in my email address.  Removing that allowed it to work.