Apparently, if you install IIS7 *after* you install .NET 4.0, you have to register .NET 4.0 manually so that you can even use it with IIS…

When multiple versions of the .NET Framework are executing side-by-side on a single computer, the ASP.NET ISAPI version mapped to an ASP.NET application determines which version of the common language runtime (CLR) is used for the application. The ASP.NET IIS Registration Tool (Aspnet_regiis.exe) allows an administrator or installation program to easily update the script maps for an ASP.NET application to point to the ASP.NET ISAPI version that is associated with the tool. The tool can also be used to display the status of all installed versions of ASP. NET, register the ASP.NET version that is coupled with the tool, create client-script directories, and perform other configuration operations.

So, here’s what got me past this issue:

C:\Windows\Microsoft.NET\Framework64\v4.0.21006>aspnet_regiis.exe -i
Start installing ASP.NET (4.0.21006).
………….
Finished installing ASP.NET (4.0.21006).

C:\Windows\Microsoft.NET\Framework64\v4.0.21006>