The problem is that the video misses the moov header which contains the details about the audio/video streams inside. Also, the header at the beginning of the file is missing.
The header at the top is rather easy to recreate by copying the first bytes from the good file and calculating the offset for the mdat part. From there on, pretty much the only option is to move over the moov section too. This results in a video file which at least opens in VLC, but it still looks buggy (it looks like you filmed something that's burning).
I have created a patch which can be applied with xdelta to the broken 3gp file: http://www.files.to/get/22295/330dkvjfmz
broken file: 96f52e415760249d9ab367f755e36f7c
repaired file: 1da0c96cd94da30466fdd7b29feab2df
You can apply the patch with: xdelta -d -s 2011-09-24_04-25-32_612.3gp repair.delta 2011-09-24_04-25-32_612-PATCHED.3gp
Maybe this will help you some; I don't really do much video editing, so the number of video programs I have is limited. Since you already tried a lot, maybe one of those programs can work with the patched file.