Hi esri inc,
I've seen this error a few times, and it almost always seems to be something to do with the Application Pool/ .NET framework settings in IIS.
I'd try the following two things:
In IIS Check your application Pool Settings for the "ArcGISWebAdaptorAppPool" and bring up its advanced properties. Click the Identity field, and change it to use something different than the "ApplicationPoolIdentity." I normally start by changing it to network service, and if that doesn't work, I switch it to Custom account, and provide it with my domain account as a test. (There are security implications for changing this, especially if it's public facing, so I'd probably check with the local IT folks to make sure they're OK with the changes.)
The second thing I'd check would be to change your .NET Framework, and if it's set to 4.0 change it to 2.0.
Lastly, while not a solution, one way to check to see if it's an IIS settings issue is to download the Windows version of Tomcat, http://tomcat.apache.org/ and install the Java Web Adaptor onto Tomcat. (To do this you'll have to stop IIS for the duration of this test/workaround.
Hope this helps!