This is the official response from Chevrolet regarding the Build Your Own option on the website:
"We apologize for any inconvenience you have experienced while attempting to build the 2014 Corvette Stingray on our website. The 2014 Corvette Stingray is scheduled to begin production in the third quarter (July, August, or September) of this year. No specific production date has been announced, and no information regarding when the website functionality will be updated. We believe that as we near the scheduled start of production, more tools and options will appear on the 2014 Corvette Stingray webpage. We encourage you to keep visiting
http://www.chevrolet.com to check for updates."