I had the exact same issue. I went through the following trouble shooting (*) and not a single thing worked. Some of the stuff I knew to do myself, other things I found online. I have to call them back tonight to get them to swap me for another one. I ordered 2 new iPod touches, and the other one works perfectly fine. After doing the complete reset on the device I logged in using my Apple ID instead of my daughters, and it still didn't work.
(*)
- Did the Soft Reboot first, which consists of holding down lock key and home key at the same time for 10 seconds until the phone reboots.
- Checked in the Date / Time under settings that it was set to Automatic.
- Reset Network Settings via the phone.
- Reset All Setting via the phone.
- Erase All Content and Settings via the phone.
- Logged out of iTunes & App Store and did soft reset on phone. Then powered back on and logged back in.
- Completely did a reset and software reload via iTunes.
- Connected via my home wi-fi, my work wi-fi & from my iPhone via tethering.
- Left on over night for over 24 hours. (I read that sometimes it just needs time.)
- Change the wi-fi DNS to 8.8.8.8.
As you can see, I tried just about everything, but nothing works. It has to be a device issue. My first call to Apple the girl was very helpful and knowledgeable on the troubleshooting procedures, but I already did most of them. The second call that I placed today to 1-800-MY-APPLE, the girl didn't seem to know what she was doing. She said after talking to a supervisor that she was going to swap out my device that I just purchased only 3 days ago. I said that would be fine. Even though I got that in under a week, she said it would take 2 weeks or more to get my replacement. I asked if it would be a new device and she said it would not, and that it would be refurbished. I was in shock and ******! She said, after speaking with a supervisor that it would be a new one. I'm not sure if I would know either way I guess, but still. I hope, even though that I didn't have a solution for you, that I saved you time on going through all these. At this point I'm going to wait patiently for a software update in the next month or so.