why won't my video button record?
Tapping the video's red circle icon just quickly highlights and then returns to previous state without recording.
iPad 2 Wi-Fi, iOS 5.1
Try closing the Camera app completely and see if you can record video when you re-open it : from the home screen (i.e. not with Camera 'open' on-screen) double-click the home button to bring up the taskbar, then press and hold any of the apps on the taskbar for a couple of seconds or so until they start shaking, then press the '-' in the top left of the Camera app to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.
If that doesn't work then you could try a reset : press and hold both the sleep and home buttons for about 10 to 15 seconds (ignore the red slider), after which the Apple logo should appear - you won't lose any content, it's the iPad equivalent of a reboot.