There is a problem with the markup in the payment section.
When the shipping method step is completed this js should be executed:
response.update_section.name is payment-method
returns null because there is no element with that id in your DOM.
Make sure that this file in your theme checkout/onepage/payment/info.phtml has the following content:
<dl class="sp-methods" id="checkout-payment-method-load"> <!-- Content dynamically loaded. Content from the methods.phtml is loaded during the ajax call --> </dl>