Have you tried to turn off all the encryption stuff and other security features of your Cisco AP? If it works then turn on one service at a time and check the configuration of the service that breaks connectivity.
Qute frankly, I would put that WiFi shiled into the recycling bin.
The design of this shield is many years old and uses an embedded TCP stack that is not trivial to handle. I'fe tried this shiled almost 3 years ago and while I fibnally got it to connect, and send UDP packages, I ran into one obstacle after another.
In the meantime I have foud the most reliable solution is an Ethernet Shield comnnected to a WiFi ppocket route such as the TP-Link TL WR703n (or 702 or 3020).
If it needs to be physically smaller then use a Teensy (www.pjrc.com) connected to a WIZ820io.
Other than that a CC3000 perhas from Adafruit may do the job and is better software supported.