iOS6 on iPod Touch (4) no Wi-FI LAN, when there is no Internet?

Well, I'll take a crack at this one. I see three possibilities: 1) the packets are not leaving the iPod; 2) the packets are being dropped somewhere along the path; 3) there is a DNS related issue.

Lets start with DNS.

From the iPod try connecting to the Intranet server using the Intranet server's IP address instead of its name. If this works than either the DNS setting in the iPod's association to the WiFi network is incorrect or the search domain is incorrect. You can check this by going to Settings->WiFi->your_wifi_network_name. If these look incorrect, try to "Forget this Network" and then reconnect.

If you still have the problem then it gets a bit more tricky

Go the App Store and get an nslookup app and a traceroute app for your iPod. Several are free and work fine. Make sure neither of the apps require a internet connection to work. Once you have the apps, open the nslookup app and enter the DNS name of your Intranet server (ex. www.myserver.local). It should return the internal IP address of the server (i.e. it should not return the internet reachable address (if it even has one)). If it does return the correct address then take that address and use it as the input for the traceroute app. The traceroute should tell you all the IP hops it takes to get to the Intranet server. If it gets so far and then stops without getting to the Intranet server's IP address then we have a network problem to troubleshoot. If it does then we have an Intranet server problem to troubleshoot.

If traceroute gets all the way to the Intranet server then turn on the detailed connection logging on the Intranet server. Then, from the iPod, try to connect to the Intranet server. Now, look at the log file on the Intranet server and see if you see the iPod IP trying to connect and if so, what error is generated. Troubleshoot the error.

If traceroute does not get the Intranet server then turn debug logging on the network devices that sit between the iPod and the Intranet server. The traffic is making it somewhere and then being dropped. Find where it is being dropped and troubleshoot why it is being dropped.

NOTE: If traceroute never leaves the iPod and/or you do not see traffic on the first device that the iPod is connected to then the problem may be within the iPod itself. If that is the case then gulp do the normal iPod stuff like reset it/reload it/etc. (I hate it when someone tells me to do that!)

I hope this was of some help to someone and that I didn't ask you to chase a red herring