We have iPhoto and Mavericks - Cannot play video and get error (OSStatus error -54). Have run permissions and rebuilt iphoto database.. This is most valuable 3 minute movie file I have... Help

Question

Has anyone a clue how I can save myself from losing most valuable video clip I have ever taken.? Have a fully up to date Macbbok pro retina and most recent iPhoto. Had 55,000 pictures and a few videos in iTunes database. Just a few months ago also installed iCloud. Now find my London Big Ben Fireworks shot of fireworks at midnight coming from clock just returns -54 error when I click it to play. Did a rebuild and permissions attempt at fixing without success. The front picture of start of video shows at start of pictures but only error box now pops up.
I had a time machine backup that goes back some months and a old computer it may have been on but have not found it yet.
I do not want to risk losing anything.  We are just finishing cruise of England and Med on our small boat-home and do not want to lose photos of our memories. Thought they were safe since in iTunes and backed up to TIME machine, and now learn they cannot be pulled out separately... Can anyone help us?
Thanks. I am grateful for any help or ideas while we float out the winter here in England before trying to sail back to America next year.
Happy Holidays.

Answer 1

I could not find the original file.
I did find a file folder named MASTERS.
I did click down in it to where all the other original files seem to be listed in order.
They are listed in files showing (name); (date modified); (date created); (size); (kind); and (date added)
There is a symbol showing each file type, with one file type for photos and a separate symbol showing the movies before each file.
All of them that are showing properly are listed in order with their name sequentially, ie:
DSCN4738.JPG
DSCN4739.JPG
DSCN4740.JPG
DSCN4742.MOV
DSCN4743.MOV
DSCN4744.MOV
My valuable movie that now won't play is shown in iPhoto viewing page listing labeled DSCN4741.MOV
I think I find it later...
OUT OF SEQUENCE APPROXIMATELY 14 files later I show the file that is shown on the listing info when viewing now named
New Years Eve Fireworks.MOV  1/1/12 Jan 1, 2012, 12:58 AM  258.1MB  QuickTime file  Feb 21, 2013, 3:46 PM
NOTE: The creation time is exactly where it should be in sequence but camera taken with was off an hour
Also, all files in list show the Feb 21, 2013 date - which is date Apple Store migrated my old computers files, which would have included my iPhoto library from my old MACBOOK PRO to the new one.
I do now remember that in past I had played some of the files from the computer by clicking on them directly in the early hours of the morning - showing some of them to a friend - while messing around demoing this MacBk Pro Retina...
Though I do not have a clear recall of it recall earlier having a hard time finding this file. I am now certain - based on the circumstantial evidence - I must have changed the name from DSCN4741.MOV to the name shown at the first line of the listing two paragraphs up.
Now my quandary is how do I escape this mess I made for myself and restore it. I clearly am -- despite being 68 -- being more of a "script kiddie" than a "hacker", but not a competent one of either!
Thanks for your help in analyzing this Terence, and hope you can help me fix my screwing it up.  Ed