I'm having almost same behavior with already-working project and FederatedAuthentication.WSFederationAuthenticationModule.
Problem solved my switching from IIS Express to full IIS (bad merge of for project file).
Also you can try to add this module not only to a section, but :
<system.web>
<httpModules>
<add name="SessionAuthenticationModule" type="System.IdentityModel.Services.SessionAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" />
You may refer to this MSDN article for a sample.