The server OS is Microsoft Windows Server 2008 Enterprise Edition x86 32 bit and it has Microsoft IIS 7 on it.
The installation guide states that on selecting the Basic installation type, the installer should present an option to select either Oracle Containers for J2EE (OC4J) version 10.1.3.1 or Microsoft IIS, if IIS is installed on the server.
However, when you run the installer, you are not presented with this option.
Install guide says:
To deploy Oracle BI Presentation Services and Plug-in with Microsoft IIS 1 Choose Advanced or Basic installation type.
2 After you select the components to install, and if Presentation Services or Presentation Services
Plug-in are selected, you are prompted to select the application server.
Select Microsoft IIS.
The ISAPI plug-in is installed in IIS.
3 When the Basic installation type is selected, the installer installs a stand-alone version of OC4J and deploys Oracle BI Systems Management and Oracle BI Publisher in this container.
However the screen does not appear in order to select IIS.
IIS 7 not properly installed
You need to check that IIS7 is properly installed in that the following services are present and enabled:
The installer checks that IIS is installed by checking that IISADMIN and W3SVC services are present and enabled.
IISADMIN service is only available if you have IIS 6 Management Compatibility options installed.
So install IIS6 Management Compatibility options for IIS7 and try again.
Business Intelligence Server Enterprise Edition – Version: 10.1.3.4.2  and later [Release: 10g and later ]
Information in this document applies to any platform.