Issue with the external harddrive?

Have you checked Finder > select external HDD >> GET INFO >>> Format and Sharing & Permissions yet?

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Strange though, that you can open the files on the external HDD but not copy from it, since it is the same process (READING).

As for recording it, which will be a loss in quality (and I guess you do not have a backup), you can use ScreenFlow, QuickTime Player X, iShowU HD, Camtasia and probably others.

Maybe also use one of the following applications to tell us what codec the videos use.

• VideoSpec (free)
• MediaInfo (free)
• Media Inspector (2.99 USD € in the Mac App Store (MAS))

When done, you can use the "Report" (VideoSpec) and "Export" (Media Inspector) button to export a report,
attachable to your next post via the button.
In MediaInfo you have to go to the Menu Bar, select View > Text and copy the text via CMD+A > CMD+C and paste it via CMD+V into your next post.​

 

And what does it say under Format and Sharing & Permissions?
Or do you mean something else?

Does that refer to another thread? There is no link, or am I confused?
Ah, had to look for myself: http://forums.macrumors.com/showthread.php?t=1521597

And what about the applications I mentioned?


Maybe take a look here:

"How to maximise your MacRumors troubleshooting experience" created by mad jew in 2006​

Anyway, since one thread per issue does suffice, I answer here to this:

If an HDD does fall, it can be damaged, especially if it was running.
But normally files do not restore themselves, thus you either had a company do that or someone else did that.
As for copying, did you try CarbonCopyCloner or SuperDuper! (CCC has a free trial and there is also a free older version available for download) to clone selected contents to another HDD?

And by "import" I guess you mean a copy process you initiated via Finder?

And again, I guess you did not employ any backups?

 

You can open them in Quicktime and view them OK? What if you try File > Duplicate (and then close to prompt a Save alert) or File > Export.. to save a copy of it?
VLC Media Player also has a streaming -> save to file option which, if you can view it, you can usually save from it.

If that approach fails, diskwarrior is a really great tool for rebuilding/recovering data from wonky drives. Not cheap though.