Fooling around with a static IP will probably just make your problem more difficult to solve. You said that it will connect to another network, right? Wasn't that with a dynamic IP? If so, that shows that your problem is not the iPad failing to use a dynamic IP configuration correctly.
What usually works with Windows, and may work with the iPad, in this situation is to disable encryption on the router and connect. Assuming the connection is successful then re-enable encryption and reconnect.
What usually works with Windows, and may work with the iPad, in this situation is to disable encryption on the router and connect. Assuming the connection is successful then re-enable encryption and reconnect.