Should be noted that Cryptolocker mimics this behavior. The progressive nature of more and more files being inaccessible is characteristic of the virus. If you see random text files in the folder. There is a good chance that you've been hit with Cryptolocker.
Also, do not copy and paste. If your drive is worn and most likely fragmented, copy+paste will cause the heads to jump around the drive and accelerate the failure. An offline cloning (disk-imaging, sector-by-sector) will be the best way to get a backup. Since you have no issues with the AC application, I'm leaning towards the possibility of the Cryptolocker virus.
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