I'm a relatively new Mac person, and have never seen this behavior before on any system.
I turned on my iPad and it asked for a WiFi password. I have a long passphrase protecting my network so I entered it carefully. Several times. No joy. It sees the network, but won't accept the password.
Now I have a Windows desktop machine, a MacBook, and iPhone, and an iPod in addition to my iPad. All of them are working.
So I took down and completely reset my router, using the same SSID and password, after rebuilding it with a different one. Everything still works except for the iPad.