OK (assuming you have your library all sorted) you can use LazyTV to have a random playlist of their TV shows playing whenever they switch on the computer. It will play the next unwatched episode of each series (rather than just any unwatched episode).
Add this to line 566 of the file called service.py in the addons folder. This will make sure the random playlist starts when XBMC is started. Make sure the code is aligned with the lines 565 and 567.
Code:
xbmc.executebuiltin('RunAddon(%s)' % __addonid__)
In the settings for the addon, set the Primary Action to be "Create and Launch Randomised Playlist. Then go to the Random Player page of the settings and set it up how you want. You can include random unwatched movies in the playlist if you like, and there is even a setting that will start the playlist with the last partially watched episode if they stopped part way through. You can set the number of episodes in the playlist.
If their tv is CEC capable, then you can set the option in XBMC to pause the video they are watching if they change the channel or switch off the TV.
Are they likely to be switching off the computer after watching their shows? Or will it be on permanently? If they leave it running then LazyTV may run out of episodes and another workaround would be required.