Autofac not resolving constructor parameter for WebAPI2 controllers

Question

I'm trying to use Autofac for DI container for an Asp.Net MVCApplication with WebApi2 and OWIN. My global.asax.cs has nothing in the Application_Start(). My startup.cs has the following Configuration:

public void Configuration(IAppBuilder app)
{
    DependencyInjectionConfig.Configure(app);

    AreaRegistration.RegisterAllAreas();
    FilterConfig.RegisterGlobalFilters(GlobalFilters.Filters);
    RouteConfig.RegisterRoutes(RouteTable.Routes);
    BundleConfig.RegisterBundles(BundleTable.Bundles);
}

And DependencyInjectionConfig.Configure is:

public static void Configure(IAppBuilder app)
{
    var config = new HttpConfiguration(); //this means webapi controllers don't use DI container
    //var config = GlobalConfiguration.Configuration; //this makes MVC view controllers fail to do anything


    var builder = new ContainerBuilder();
    var assm = Assembly.GetExecutingAssembly();

    //MVC and WebAPI Controllers
    builder.RegisterControllers(assm);
    builder.RegisterApiControllers(assm);
    WebApiConfig.Register(config);

    //Model Binders
    builder.RegisterModelBinders(assm);
    builder.RegisterModelBinderProvider();

    //Modules
    builder.RegisterModule<AutofacWebTypesModule>();

    //MVC Views
    builder.RegisterSource(new ViewRegistrationSource());

    //MVC and WebAPI Filters

    builder.RegisterFilterProvider();
    builder.RegisterWebApiFilterProvider(config);

    //Finally, Any custom registrations
    RegisterComponents(builder, assm);
    /* My items show in the builder as expected at this point */

    //build the container
    var container = builder.Build();
    DependencyResolver.SetResolver(new AutofacDependencyResolver(container));
    config.DependencyResolver = new AutofacWebApiDependencyResolver(container);

    //Special OWIN bits
    app.UseAutofacMiddleware(container);
    app.UseAutofacMvc();
    app.UseAutofacWebApi(config);
    app.UseWebApi(config);
}

My problem is that Autofac does not seem do any parameter resolution regardless of if I use var config = new HttpConfiguration(); or var config = GlobalConfiguration.Configuration;. bonus, if I use GlobalConfiguration.Configuration MVC controllers for views completely fails.

The ApiController is pretty straight-forward:

public class MessagesController : ApiController
{
     private IMesageHandler MessageHandler {get; set;}
     public MessagesController(IMessageHandler messageHandler)
     {
         this.MessageHandler = messageHandler;
     }
     [HttpGet]
     public string Get()
     {
         return "Hello World";
     }
}

The exception is that it can't find a parameterless constructor (because the Autofac container appears to be napping).