I experienced this situation on our development system after applying the 1.2.5 ThemeBurn update. When the user is logged in with products in the shopping cart and selects the “Checkout” button they are transferred to the Checkout page, however the Checkout Option #2 (Billing Details) does not expand. There is no control on the right side to expand, no continue button.
I am putting a link to a Shoppica problem which displays a similar problem;
http://support.themeburn.com/topic/checkout-page-disappear-while-logged-in

They may or may not be associated and only coincidence.

I went back to the default theme and the problem went away. I rolled the system back to 1.2.4 and the problem went away as well.

Another characteristic that when the user was logged in and in the shopping cart, and entered “Estimate Shipping and Taxes” the “Get Quotes” button did not work. If I used Safari Inspector on the page it displayed an “Invalid Token” message on the page.

Please advise, since it is a development system I can re-install the update (1.2.5) if you want.

Thanks
Brad