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The determination needs to be made as to exactly how they were made. It is possible they were made as data DVD's and the person who made them simply put video files on them. It is also possible that the session was not closed. It is also possible that they are copyrighted DVD's and as a result will only play on the computer that made them/backed them up.
I think the next step is to see if VLC can play them.
If you do not have it loaded already, go here:
Download the latest version of VLC. Install it. Once that is complete, put the DVD into the drive on that computer. VLC should automatically try to play it. If it does not, from inside VLC, go to Media > Open Disc...
Under Disc Device select the DVD drive and click Open. See if the video plays.