Try Another PC first.
It could be a USB data pin broken inside the Nuvi as well. There are 5 pins in USB 2 data RX/TX 2 power +5v -5v and 1 resitor ID.
Try spraying the plug on the nuvi with a little bit of contact cleaner.(just a little)
To Update the Firmware, download the file from Garmin and Copy to SDCard/Garmin/Gupdate.gcd (Maybe it will work on 765)
You can copy maps and POI to memory card. So even if the USB is not working you might be able to survive.