Have you got any videos or tv shows on the iPad ? If you have then try searching for the name of one of them on the iPad's spotlight search screen - swipe your first homescreen to the right, type in it's name, and if it finds it tap on it to see if it plays.
If that doesn't work then try closing the Videos app completely : from the home screen (i.e.not with the Videos app '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 Videos app to close it, and touch any part of the screen above the taskbar so as to stop the shaking and close the taskbar.
A third option if the two above don't work is 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.
This happened to me recently and I tried everything I was able to see on various forums like this. Nothing worked. Finally I connected my iPad to my computer, brought up iTunes, went to My iPad under Devices on the computer screen, highlighted the video I had been trying to watch and deleted it. Immediately the Video App was restored to normal.
I have heard since that this problem may come about when a video is downloaded by WiFi, which was the case with the video I had tried to watch when my video app went blank. So I re-loaded the same video on my computer (not WiFi) and now I can watch it with no problems.
Hope this helps.