Hopefully this helps someone else. I have posts in other threads about my issues connecting to wi-fi at home.
I logged in to my router, and at first just disabled the security. The iPad2 connected to the internet, no problem. It was using WEP, and I understand WPA2 is supposed to be more secure so re-enabled security with that instead.
Entered the new password into the iPad, and bingo! Problem solved. Apparently the iPad doesn't like WEP security. No matter what I did when the WEP security was enabled it would not connect nor would it hold the proper IP address.
I've already had it connect to 2 different public wi-fi spots so for now all is good.
What I have not done yet is upgrade the firmware - right now it's on 4.3.3, though iTunes has already indicated 4.3.5 is available. I'm ascared to update it now, LOL.