After five pages of Q&A with Peacedog (he's now my hero) I got my usb wireless-n adapter to work. The solution was so simple I could kick my self.

My router, D-Link DIR-628, has two passwords. One is for the network itself and the other for the wireless security. When trying to connect using wireless and WPA/WPA2 security, make sure you enter the WPA/WPA2 password, NOT the network password. I still have wireless security (WPA) and I have wireless-n on my Ubuntu box.
So if you can't connect wirelessly:
First disable all wireless security to make sure the adapter is working correctly.
Second, enable WEP security and enter the WEP password, NOT the network password, as part of the setup. IF that works, then...
Third, enable WPA-Personal security and enter the WPA-Personal password.

Thanks again to Peacedog for his help & patience.