Can anyone help me with this file transfer problem?

THE SETUP
I have a 150 GB external HDD connected via FireWire 400. My friend has a 120 GB external HDD connected via USB 2.0. They both have external power adapters. They are both formatted in MS-DOS Fat 32 and were connected to my MacBook.
THE PROBLEM
I tried to transfer some video files (.AVI) from my friends HDD to my HDD. It was about 30 GB's worth of files (made up of about 150 - 200 files (each about 100 MB's - 300 MB's in size). The copy window said it should take about 30 minutes. After about 5 minutes into the transfer, my MacBook just shut off. I restarted, tried again and it shut off again after the same amount of time.
THE QUESTION
What is the problem?
P.S. - If any one needs me to elaborate about anything posted above then just post what you need and I'll be glad to provide more info. (I'm very upset, tired and embarrassed. Which means that I'm not thinking straight.) ~_~
Thank You in advance for your input and help.

UPDATE
Now, every time I try to watch the videos from my external HDD, my computer shuts off after about 2 minutes. I watched one whole 22 minute video while my HDD was connected via FireWire. When I tried to watch another video, my computer shutdown after 2 minutes. After several attempts to watch the video, on a whim I decided to connect my HDD via the included USB 2.0 cable. As I suspected, the entire second video played without a single problem. When I went to watch the third video, guess what, my computer shutdown again after about 2 minutes of playback.
I was using Front Row to watch the videos. I did get the third video to play in Quick Time, but when I tried to play the fourth video (in QT) my computer shut off after about 2 minutes of playback. All of the files are .AVI video files with a resolution of about 640 X 480.

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