iPod Touch 3G: DOA

After many hours of troubleshooting, and then two calls to Apple Help, my new iPod Touch 3G is officially pronounced DOA. What happens is that it has no problem connecting with a Wi-Fi network, but seconds later downloads stop. The status bar shows that there is an active connection, but no packets are received.

I tested this both on my home network and the local library's Wi-Fi network with the same result.

Apple will be shipping me a new one, as soon as I can send back this lemon.