General help

Your issue may be different, even if the result is the same. Have you compared the file sizes? Do you have the same 10 byte change in size? Was it working then stopped? Have you still got the original files, or do you only have the ones uploaded? Are the original OK or are they corrupt too? Better look I suggest. 

My early suspicion would be that the php files that handle downloads have not been properly loaded in the core code base, and as I don't know which specific file or files that may be, better off replacing all with an update of the Moodle. try a 2.7.5+, being the latest in that range. There should not be too much of a drama, to replace the files, just make sure your existing config.php file is clean and not overwritten. (Copy it off somewhere else, open it in a UTF-8 compliant editor, like Vi or Notepad++ in Windows  or similar in Mac, and try to delete everything after the last line of text, or any other characters that do not relate to the code or the Moodle. Such an update refreshes everything and if handled correctly, the post-update testing will take longer than the update itself.