I also had this problem with a 6th gen nano. I did register it on apple.com, but iTunes still prompted me to register. I chose the register later option and it let me through, but then when I tried to sync for the first time, iTunes would freeze almost immediately and then my computer would crash. I ended up unistalling and reinstalling iTunes altogether.
After that, iTunes did not show the device so I had to restart the iPod service. (windows 7 - Control Panel; System & Security; Administrative Tools; Services; iPod service). Make sure the iPod is disconnected from the computer, then stop the service, reconnect the iPod, then start the service again. After I did that, it showed up in iTunes and miraculously, it synced w/ no problem.
Oh...and it let me register! No more "You must complete the entire form" message!!
I hope this helps!