Do you have any wireless devices already using the BT router, or is the iPad the first you've tried to connect?
If the iPad is the only wireless device, make sure the BT router is set to use WPA2 security (WPA2-PSK - WPA2 Pre-shared Key).
If the iPad is not the only device, check to make sure the other devices support WPA2 before changing to it (if it's not already set to WPA2). If they don't support it, try WPA instead. Don't use WEP.
Try changing the network name (SSID) of the BT router to something else, as well as changing the WiFi password.
Try disabling the wireless security on the BT router - temporarily - to see if the iPad will connect without it. If it works, re-enable the security and set a new password. Do not leave the security disabled