First, you need to know a .mov file is not really just one type of file. A .mov file is a container of audio and video streams that can be encoded in a variety of ways. Some of them may not work in Quicktime Player even though that is usually what tries to play them.
To make sure the files actually contain valid video, you might try a different program to play them. VLC is a free program that is kind of the Swiss army knife of video players. It will play almost anything.
Next, you may want to convert them. VLC has some capabilities in this regard but there is another program that is even better that is called Handbrake. I will warn that it has a bit of a learning curve, but it is a rather versatile transcoding tool for converting videos into different formats.
I can tell you more about them if this sounds like something you want to pursue.