Product:
Cognos Controller 10.3
Microsoft Windows 2012 R2 server

Problem:
When starting the Cognos Controller client for the first time in a new installation, you get a error like this:
An error occurred while trying to access the server.
Details give:
The request failed with HTTP status 405: Method Not Allowed.
at System.Web.Services.Protocols.SoapHttpClientProtocol.ReadResponse(SoapClientMessage message, WebResponse response, Stream responseStream, Boolean asyncCall)
at System.Web.Services.Protocols.SoapHttpClientProtocol.Invoke(String methodName, Object[] parameters)
at Cognos.Controller.ControllerSoapHttpClientProtocol.Invoke(String methodname, Object[] parameters)
at Cognos.Controller.Proxy.Light.WSLight.CheckServerConnection(String sGuid, String sUser)
at Cognos.Controller.Direct.ServerInfoD.CheckServerConnection()
at CCR.AppContext.CheckConnectionToServer()

If you start Internet explorer and surf to
http://APPSERVER:80/ibmcognos/controllerServer/ccrws.asmx
you get a HTTP error 404

Solution:
Ensure that on the Cognos Controller server you have installed windows roles for .NET extensibility 4.5 and ASP.NET 3.5 and ASP.NET 4.5 under Application Development for IIS server role.

This show some of what need to be in the Windows server to make Cognos Controller work:
http://www-01.ibm.com/support/docview.wss?uid=swg21986254

More information:
http://www-01.ibm.com/support/docview.wss?uid=swg21653361