Many, many thanks for your offer. I actually have a support topic going here:
http://discussions.apple.com/thread.jspa?threadID=1928799&tstart=0
However, please note: I think you misunderstood -- Both my G1 and G2 iPod Touches work on my secured network at home. My G1 Touch does a pretty good job of joining unsecured networks (both public and private) around town, but my G2 Touch has never yet succeeded in joining an unsecured network.
And -- this is my second G2 Touch. I returned the first one because of this wifi issue and another problem. In my replacement G2 Touch, the other problem is fixed, but the wifi issue is identical.
Thanks again.