I can get the phone to find the WiFi networks and connect. However, it does not work at all -- Weather, Safari, YouTube, etc.
It displays the wifi signal on the homescreen.

It was working fine before the SW Unlock.

This is an unsecured wifi network in my home and I am using 2 other computers fine.

I tried doing a full restore using iTunes, reactivated the phone, and still no WiFi.

It is firmware version 1.0.2 and iTunes 7.3.

Any suggestions?

Why dont u try This ,

turn airplane mode on/off for 30 seconds , then
go to > Seettings > general > Reset > Reset network setting . restart the phone and go to wi-fi seeting and join the network ,
if DHCP and Statis setting are having IP address , u shld be able to get wi-fi up and running .