If you decide to use ffmpeg you will need to learn some .
I've played with ffmpeg & still consider myself a novice with it.
I do think I got some better quality with ffmpeg than AVStoDVD with the .mp4 I used. It may not be the same with the "damaged" file you are working with.
To correct TSJnachos117 it won't work with quotes or spaces in the file names input or output.
If you use the code he used it would be like this:
ffmpeg -i input_file.mkv -vcodec copy -acodec copy -aspect 4:3 output_file.mkv
You will also need to paths to the input file as you will see in the code I use.
For me the output file is in my C:\Program Files\ffmpeg\bin . That's where ffmpeg puts it if you don't specify another location. To me this is just easier.
This is the code I used:
ffmpeg -i C:\VIDEO\input_file.mp4 -s 640:480 -aspect 4:3 -c:v libx264 -preset medium -x264-params crf=25 -c:a copy output_file.mkv
This uses the medium quality setting .H264 codec .
Controls the output ratio to a true 4:3 .
Note you can try 720 instead of 640 .
There are some pixel shape settings in additional code .
I tried what I could find but saw little difference.
If I knew more I might be able to use those settings correctly.
Their are higher & lower settings for quality but I think you will find Medium fine especially with a "damaged" video.