I hadn't used my iPad in some time, and recently tried powering it back on. As soon as iOS starts up, I am prompted to enter my iCloud password. My home WiFi network has changed since the last time I used the iPad, so there is no internet access. The iPad won't accept what I believe to be the password for my Apple ID the last time I used it (I have since changed it, but imagine it's expecting me to enter a cached password since the device hasn't been in contact with Apple's servers in some time).
I'm unable to connect to my new WiFi network since the iCloud prompt appears every second after hitting cancel. Is there any way out of this loop? I've tried restoring the device via iTunes, but it tells me that that Find my iPad has to be disabled before doing a restore (which, of course, requires entering the iCloud password).