Just to give you an update, I got the iOS 3.1.3 installed (Even with the error messages 1602 & 1604). This is how I did it.
1. Turn off all spyware and antivirus
2. Open ITunes and purchase iOS and download (don't connect you ipod to the computer yet), don't select download and install. Close itunes after download.
3. My ipod was frozen with the connector and iTunes symbol in the screen, so I turned it off and with the usb plugged into the computer, hold the home button down (Puts it in recovery mode), now connect the end of the sync cord to the ipod, open iTunes and let it boot up. You should see the message that it found an ipod in recover and need to be restores. click ok and then select update.
4. This is where it will update and freeze again in restore. To continue update, leave the ipod connected (Don't touch it at all. Close iTunes and then reopen it. The connection should be made the the update should install.
It worked for me, maybe it will fro yo.