.MOV is a container format (like .AVI). The actual encoding of the movie can be almost anything.
Do Comand-I on both computers to verify that the file is not corrupted. And post here what the video encoding is.
For example, when I make a movie in iMovie I use Mpeg-4 since it can be played on just about anything. When I do CMD-I on it I get:
"H.264" is the video encoding (or Codec), "AAC" is the audio.
See what you have.
Heh. I guess I have to also ask if your computer can display 1080p HD movies too!
This is the video and audio file formats Quicktime supports
The open source Perian project has stopped, they used to provide a System Preference pane that would add additional codecs to Quicktime.
So now for playback you will need to use open source VLC, and perhaps some other programs to convert the video and audio files into formats that Quicktime will support if your planning on editing the files in iMovie, etc.
Since the inception of OS X 10.7 and the MacAppStore basically not allowing OpenSource software (all MAS software has to be copy protected) it seems Apple and Mac's are consistantly being forgotten now by the Open Source community.
Gone are the reference links to Apple on Slashdot, gone are great programs like Perian and AppleJack, gone is a VLC version for OS X on the front page, now it's hidden on another page and likely not being updated much anymore.
So I don't know how much longer VLC is going to work on 10.7, it's for 10.5 and later.