the biggest thing I see is that you don't have a "system.identityModel" section defined. (my third code block below)
i have one that works...here are the differences I see:
<system.web>
<authentication mode="None" />
and (note the remove)
<modules runAllManagedModulesForAllRequests="true">
<remove name="FormsAuthenticationModule" />
<!--WIF 4.5 modules -->
<add name="SessionAuthenticationModule" type="System.IdentityModel.Services.SessionAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>
<!-- Adding the below causes a "ID0006: The input string parameter is either null or empty. Parameter name: Issuer" error -->
<!--<add name="WsFederationAuthenticationModule" type="System.IdentityModel.Services.WSFederationAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>-->
</modules>
and (I do a "clear", but you could do a remove and add (same object))
<system.identityModel>
<identityConfiguration saveBootstrapContext="true">
<securityTokenHandlers>
<clear /> <!-- Note the CLEAR here -->
<add type="System.IdentityModel.Tokens.SessionSecurityTokenHandler, System.IdentityModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089">
</add>
</securityTokenHandlers>
</identityConfiguration>
</system.identityModel>
Here is my full file, just in case:
<?xml version="1.0" encoding="utf-8"?>
<!--
For more information on how to configure your ASP.NET application, please visit
http://go.microsoft.com/fwlink/?LinkId=169433
-->
<configuration>
<configSections>
<!-- For more information on Entity Framework configuration, visit http://go.microsoft.com/fwlink/?LinkID=237468 -->
<section name="entityFramework" type="System.Data.Entity.Internal.ConfigFile.EntityFrameworkSection, EntityFramework, Version=5.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089" requirePermission="false" />
<!--WIF 4.5 sections -->
<section name="system.identityModel" type="System.IdentityModel.Configuration.SystemIdentityModelSection, System.IdentityModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089" />
<section name="system.identityModel.services" type="System.IdentityModel.Services.Configuration.SystemIdentityModelServicesSection, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=B77A5C561934E089" />
</configSections>
<connectionStrings>
<add name="DefaultConnection" providerName="System.Data.SqlClient" connectionString="Data Source=(LocalDb)\v11.0;Initial Catalog=aspnet-SessionAuthenticationModuleQuickDemo-20151014083716;Integrated Security=SSPI;AttachDBFilename=|DataDirectory|\aspnet-SessionAuthenticationModuleQuickDemo-20151014083716.mdf" />
</connectionStrings>
<appSettings>
<add key="webpages:Version" value="2.0.0.0" />
<add key="webpages:Enabled" value="false" />
<add key="PreserveLoginUrl" value="true" />
<add key="ClientValidationEnabled" value="true" />
<add key="UnobtrusiveJavaScriptEnabled" value="true" />
</appSettings>
<system.web>
<compilation debug="true" targetFramework="4.5.2" />
<httpRuntime targetFramework="4.5.2" />
<authentication mode="None" />
<pages>
<namespaces>
<add namespace="System.Web.Helpers" />
<add namespace="System.Web.Mvc" />
<add namespace="System.Web.Mvc.Ajax" />
<add namespace="System.Web.Mvc.Html" />
<add namespace="System.Web.Optimization" />
<add namespace="System.Web.Routing" />
<add namespace="System.Web.WebPages" />
</namespaces>
</pages>
<profile defaultProvider="DefaultProfileProvider">
<providers>
<add name="DefaultProfileProvider" type="System.Web.Providers.DefaultProfileProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</profile>
<membership defaultProvider="DefaultMembershipProvider">
<providers>
<add name="DefaultMembershipProvider" type="System.Web.Providers.DefaultMembershipProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" enablePasswordRetrieval="false" enablePasswordReset="true" requiresQuestionAndAnswer="false" requiresUniqueEmail="false" maxInvalidPasswordAttempts="5" minRequiredPasswordLength="6" minRequiredNonalphanumericCharacters="0" passwordAttemptWindow="10" applicationName="/" />
</providers>
</membership>
<roleManager defaultProvider="DefaultRoleProvider">
<providers>
<add name="DefaultRoleProvider" type="System.Web.Providers.DefaultRoleProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" applicationName="/" />
</providers>
</roleManager>
<!--
If you are deploying to a cloud environment that has multiple web server instances,
you should change session state mode from "InProc" to "Custom". In addition,
change the connection string named "DefaultConnection" to connect to an instance
of SQL Server (including SQL Azure and SQL Compact) instead of to SQL Server Express.
-->
<sessionState mode="InProc" customProvider="DefaultSessionProvider">
<providers>
<add name="DefaultSessionProvider" type="System.Web.Providers.DefaultSessionStateProvider, System.Web.Providers, Version=1.0.0.0, Culture=neutral, PublicKeyToken=31bf3856ad364e35" connectionStringName="DefaultConnection" />
</providers>
</sessionState>
</system.web>
<system.webServer>
<validation validateIntegratedModeConfiguration="false" />
<handlers>
<remove name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" />
<remove name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" />
<remove name="ExtensionlessUrlHandler-Integrated-4.0" />
<add name="ExtensionlessUrlHandler-ISAPI-4.0_32bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness32" responseBufferLimit="0" />
<add name="ExtensionlessUrlHandler-ISAPI-4.0_64bit" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" modules="IsapiModule" scriptProcessor="%windir%\Microsoft.NET\Framework64\v4.0.30319\aspnet_isapi.dll" preCondition="classicMode,runtimeVersionv4.0,bitness64" responseBufferLimit="0" />
<add name="ExtensionlessUrlHandler-Integrated-4.0" path="*." verb="GET,HEAD,POST,DEBUG,PUT,DELETE,PATCH,OPTIONS" type="System.Web.Handlers.TransferRequestHandler" preCondition="integratedMode,runtimeVersionv4.0" />
</handlers>
<modules runAllManagedModulesForAllRequests="true">
<remove name="FormsAuthenticationModule" />
<!--WIF 4.5 modules -->
<add name="SessionAuthenticationModule" type="System.IdentityModel.Services.SessionAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>
<!-- Adding the below causes a "ID0006: The input string parameter is either null or empty. Parameter name: Issuer" error -->
<!--<add name="WsFederationAuthenticationModule" type="System.IdentityModel.Services.WSFederationAuthenticationModule, System.IdentityModel.Services, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089"/>-->
</modules>
</system.webServer>
<runtime>
<assemblyBinding xmlns="urn:schemas-microsoft-com:asm.v1">
<dependentAssembly>
<assemblyIdentity name="System.Web.Helpers" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-2.0.0.0" newVersion="2.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.Mvc" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-4.0.0.0" newVersion="4.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="System.Web.WebPages" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-2.0.0.0" newVersion="2.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="EntityFramework" publicKeyToken="b77a5c561934e089" />
<bindingRedirect oldVersion="0.0.0.0-5.0.0.0" newVersion="5.0.0.0" />
</dependentAssembly>
<dependentAssembly>
<assemblyIdentity name="WebGrease" publicKeyToken="31bf3856ad364e35" />
<bindingRedirect oldVersion="1.0.0.0-1.3.0.0" newVersion="1.3.0.0" />
</dependentAssembly>
</assemblyBinding>
</runtime>
<entityFramework>
<defaultConnectionFactory type="System.Data.Entity.Infrastructure.SqlConnectionFactory, EntityFramework" />
</entityFramework>
<system.identityModel>
<identityConfiguration saveBootstrapContext="true">
<securityTokenHandlers>
<clear /> <!-- Note the CLEAR here -->
<add type="System.IdentityModel.Tokens.SessionSecurityTokenHandler, System.IdentityModel, Version=4.0.0.0, Culture=neutral, PublicKeyToken=b77a5c561934e089">
</add>
</securityTokenHandlers>
</identityConfiguration>
</system.identityModel>
<system.identityModel.services>
<federationConfiguration>
<cookieHandler requireSsl="false" />
</federationConfiguration>
</system.identityModel.services>
</configuration>