There has been a clean install on a separate web server that does not have this same issue. The original install of the instance that's erroring had an original install date of July 2011 and has been upgraded since. The instance I've been testing against was a clone of the production instance that has the issue, so it's a good measure of what's actually wrong.
I had tried moving the guinea pig instance to the webserver that has our working demo (used the same connection string, new app pool, different web server) and it still showed that error.
I'm not sure on what's running in IIS honestly. I know that the App Pool can be changed to .NET 4 so I'm going to assume that it's registered with IIS. The DNN instance is still running on 2.0 Integrated. It was running on .NET 4 app pool and I changed it back to 2.0 thinking it may have something to do with the issue.
I compared my web.config with the instance that works and I don't find anything that's glaringly different. I could always post them up sans-connection strings if you think that's going to be a viable option.
It might be worthwhile to do a repair install of .NET 3.5 Framework and see if that fixes anything up. The thing that kind of makes me wonder, the web servers are Hyper-V instances that we have running. I'm not sure if the instances were spawned off the same VM or not. If they are, the one webserver is in a functional state, and the other isn't.
I won't be able to get back to you until after next week as I'll be out of the office but appreciate the time you've put in. Thanks!