To recreate: in your mp3 directory of your SD card, put an mp3 file that between the directory path and filename is longer than (I'm guessing around) 255 characters (I have my music folders arranged several subdirectories deep, and filenames including artist, album, year, title, etc.). Put the SD card in your nuvi 765T. Turn on nuvi 765T. Around the "updating maps" point, the unit just goes black, and it won't turn back on.
The only way to get it back on is to remove the SD card, and even then you need to wait about 10 minutes.
This would be in Garmin's best interest to fix. I had had a prior unit's battery fail and this looked very similar, and I nearly sent it back under warranty... I wonder how many units they've replaced assuming the unit was toast.
Many operating systems don't allow filename + path name > 255 characters. However, I don't know internally if things like the name of the SD card count, or some internal directory it may be mounted under. I think a directory + file of 200 characters or less under the mp3 directory would be safe but I haven't refined it exactly.