I'm experiencing the same problem as described here and my set up is almost identical to this that is actually based on this guide. When I access a method in my controller I get this
An error occurred when trying to create a controller of type 'TestController'. Make sure that the controller has a parameterless public constructor.
Here's the stack trace
at System.Web.Http.Dispatcher.DefaultHttpControllerActivator
  .Create(HttpRequestMessage request, HttpControllerDescriptor controllerDescriptor, 
     Type controllerType)\r\n   
at System.Web.Http.Controllers.HttpControllerDescriptor
  .CreateController(HttpRequestMessage request)\r\n   
at System.Web.Http.Dispatcher.HttpControllerDispatcher.<SendAsync>d__1.MoveNext()
And here's the inner exception's stack trace
at System.Linq.Expressions.Expression.New(Type type)\r\n  
at System.Web.Http.Internal.TypeActivator.Create[TBase](Type instanceType)\r\n   
at System.Web.Http.Dispatcher.DefaultHttpControllerActivator
   .GetInstanceOrActivator(HttpRequestMessage request, Type controllerType, Func`1& activator)\r\n   
at System.Web.Http.Dispatcher.DefaultHttpControllerActivator
   .Create(HttpRequestMessage request, HttpControllerDescriptor controllerDescriptor, Type controllerType)
Here's what my controller looks like
public class TestController : ApiController
{
    private readonly ITestRepo _repo;
    public TestController(ITestRepo repo)
    {
        _repo = repo;
    }
    public IEnumerable<string> Get()
    {
        return new string[] { "value1", "value2" };
    }
    public string Get(int id)
    {
        return _repo.GetId(id);
    }
}
And here's how I set up Simple Injector
 public class Startup
 {        
   public void Configuration(IAppBuilder app)
   {
      // Create the container as usual.
      var container = new Container();
      // Register your types, for instance using the RegisterWebApiRequest
      // extension from the integration package:       
      container.RegisterWebApiRequest<ITestRepo, TestRepo>(); 
     container.RegisterWebApiControllers(GlobalConfiguration.Configuration);
      container.Verify();
      GlobalConfiguration.Configuration.DependencyResolver =
            new SimpleInjectorWebApiDependencyResolver(container);
      //
      ConfigureOAuth(app, container);
      var config = new HttpConfiguration();
      WebApiConfig.Register(config);
      app.UseWebApi(config);
   }
}
                I had the same issue but with UnityDependencyResolver. But I think it should also work for SimpleInjectorWebApiDependencyResolver. Try to register your resolver like this (as a Property of HttpConfiguration):
public void Configuration(IAppBuilder app)
{
    var container = GetContainer(); // Initialise container
    HttpConfiguration config = new HttpConfiguration
    {
        DependencyResolver = new SimpleInjectorWebApiDependencyResolver(container);
    };
    WebApiConfig.Register(config);
    app.UseWebApi(config);
}
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