Tried that, after powering down the router and restarting everything and still cannot get internet connection.
Here are the network settings on the iPad:
IP Address 169.254.407.49
Subnet Mask 255.255.0.0
Nothing in the other fields.
As before, my Touch connects right away. Should I just exchange it? I'm at my wit's end with this.
The DHCP server is not giving the iPad an address. The one showing is self assigned. Besides the IP Address (usually) being in the 192.168.x.x range, you should also see a minimum of DNS and Router address entries.
You normally fix this by restarting the Router, but since you've tried two different routers with the exact same results I've got doubts this will help. Won't hurt to try if you haven't, though. Be sure to leave the router off for a couple minutes, and reset the networks settings on the iPad while you wait as a little extra help.
If you've not been able to connect to any hotspots, including free ones at places like McDonald's, I'd consider taking to an Apple Store if you can, they can test it right there. Otherwise call Apple Tech Support.
Problems with this or that router is an all too common with iPads. Failing with all routers and hotspots is not.