Did you look in the Videos App?
Try these basic troubleshooting steps and maybe one of them will help.
Do a search for one of your videos from the spotlight search. Go to the home screen and swipe to the right. The search feature will come up on the screen. Type in the name of one of your movies or videos. If it shows up in the search, tap on it and hopefully it will begin to play. If it does start playing, let it go for a couple of minutes and then tap "Done" now go to the videos app and see if it works OK.
Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
Or try this ...
Reset the iPad by holding down on the sleep and home buttons at the same time for about 10-15 seconds until the Apple Logo appears - ignore the red slider - let go of the buttons.
Or quit the videos app and restart.
Go to the home screen first by tapping the home button. Quit/close open apps by double tapping the home button and the task bar will appear with all of you recent/open apps displayed at the bottom. Tap and hold down on any app icon until it begins to wiggle. Tap the minus sign in the upper left corner to close the apps. Restart the iPad. Restart the iPad by holding down on the sleep button until the red slider appears and then slide to shut off. To power up hold the sleep button until the Apple logo appears and let go of the button.
If the very first fix works for you - remember that there is a time limit on the rental from the first time that you start the movie. I cant remember what that time limit is - but you can check and make sure that you will be watching the movie within that time frame.
Go to home screen and enter the 'search field' by swipeing from left to right. When in 'search field' start spelling the name of your show, or one of the episodes. Now, hopefully they will appear and you'll see an icon on the left to the title, to clarefy in which App they are placed.
Hope this was helpful.