I have a similar problem as the one presented in the question No Entity Framework provider found for the ADO.NET provider with invariant name 'System.Data.SqlClient'
Wow...that is pretty special...Anyways. You need to register the Entity Framework provider for the System.Data.SqlClient SQL connection type.
System.Data.SqlClient
You want to add the following to your app.config/web.config
app.config
web.config