I think Justin means the core isn't being loaded meaning there are no scripts or css from WPEC being loaded. I will allow him to comment further about that but when I view the source I don't see certain scripts and css.
That aside... Try all of the following...
1. reset your permalinks - go to permalink settings set them to default and save then set them back to your permalink settings.
2. go to the Store > Presentation tab settings and clear the template cache.
3. if this still fails to remedy the situation try the following to check for conflicts
3.a disable all non WPEC related plugins. switch to a default wWP theme such as 2010. once again clear the store template cache.
now test the store I would test by enabling the MANUAL PAYMENT method in payment settings.
If checkout completes properly then you either have a conflict with a plugin or the theme or your payment settings may be incorrect.
Lastly are you using authorize.net ARB or CIM or eCheck? If not I'd suggest switching to using the Authorize.net AIM payment option.