Product:
Cognos Analytics 11.0.13
Cognos Controller 10.4.1 (10.4.1100.133)
Microsoft Windows 2012 R2 standard server

Problem:
Surf to http://servername/IBMCOGNOS give error HTTP 403, and no Cognos Analytics page.
The website declined to show this webpage – HTTP 403 Forbidden

You may also get a error like this:
Service Unavailable
HTTP Error 503. The service is unavailable

Solution:
Above error can be that the Application Pool is using the wrong user;
1) From the Start menu, click Control Panel, and then double click to open Administrative Tools.
2) Double click Internet Information Services.
3) Right click on Application Pools and select Properties.
4) Click the Identity tab.
5) If the predefined option is set to Network Service, change it to Local System, or leave it at ApplicationPoolIdentity.

Can also be that above user do not have access to NTFS files.

Most common is that the URL rewrite rules are not created, check in IIS on /ibmcognos/bi folder to see if there are any URL Rewrite rules. If the rules are missing, then it may be because there where left overs of old virtual folders in IIS, like controllerbin or controllerhelp.

You most remove them first, then remove SSO and IBMCOGNOS – as below:
– Open IIS
– Click on Application Pools
– Select the Cognos 11 App Pool and stop it
– Stop also any App Pool for Cognos Controller
– Expand everything
– Select the ibmcognos -> controller folder and remove it
– Select the ibmcognos -> controllerbin folder and remove it
– Select the ibmcognos -> controllerserver application and remove it
– Select the ibmcognos -> sso application and remove it
– Select the ibmcognos application and remove it
– Click on Application Pools, select the Cognos app pool, and delete it
– Close IIS

Open your file explorer
– Navigate to the Cognos gateway install directory
– Delete the following web.config files:
cgi-bin\web.config
webcontent\web.config
webcontent\bi\web.config
Then you can run the CA11 install IIS script again.
https://www.ibm.com/support/pages/automate-configuration-microsofts-internet-information-service-support-ibm-cognos-analytics

More Information:
https://www.ibm.com/support/pages/how-properly-clear-microsofts-internet-information-service-iis-configurations-setup-new-configuration-iis-support-ibm-cognos

https://www.ibm.com/support/pages/request-failed-http-status-503-service-unavailable-when-launching-controller
https://www.ibm.com/support/pages/request-failed-http-status-503-service-unavailable-when-launching-cognos-iis-gateway