If your copy of Apple's iTunes software won't play TV shows, the cause of this problem is simple--you're not running the latest version of iTunes. Only iTunes version 9 and newer has the ability to play television shows purchased from Apple's iTunes digital media store. So long as your computer is connected to the Internet, you can download and install the latest version of iTunes and get your TV shows up and running in no time.
Click "Help" and then "Check for Updates." iTunes will connect to the Internet and see that there is a new version of the program available on Apple's Web servers.
Click "Download and Install." This will update your iTunes to the newest version. When the update is complete and iTunes restarts, you will be able to properly play TV shows.