Garmin nuvi 765 lithium battery will not hold a charge more than 15 minutes!

The Nuvi 780 is an older GPS. Most likely, the battery needs to be replaced due to age. Many lithium-Ion batteries are only good for 2 years. More information can be found here:

http://www.sharc.net/gps_battery_repair.htm

Please have the battery replaced by a professional. We have repaired many units from failed battery replacements by customers. Often other things get broken in the process, sometimes beyond repair.

Holding the switch does not always work. The problem is that the Garmin batteries wear out very quickly and if you don't charge them every few days they drain completely and the voltage drops to zero. The problem is the brilliant Garmin engineers designed the Nuvi 700s so that the charging circuit doesn't activate when you plug it in if the battHolding the switch does not always work. The problem is that the Garmin batteries wear out very quickly and if you don't charge them every few days they drain completely and the voltage drops to zero. The problem is the brilliant Garmin engineers designed the Nuvi 700s so that the charging circuit doesn't activate when you plug it in if the battery voltage is zero. See the Catch 22? Also, even if you replace the battery, if the new battery is not already charged, you are in the same boat! I solved it by taking the Nuvi apart and zapping the battery with 5 volts across the red and black terminals. It's very difficult because the plug has tiny holes smaller than a typical pin. You have to be very careful too because the lithium polymer battery could catch on fire or explode! I used a very low current to lessen the chance of this. After doing this for about a minute and raising the battery voltage to about 3 volts, I plugged it back in, put it back together, and it was able to charge.

Which would suggest the battery is not charged, or retaining its charge.
Will it start up if connected to a power supply (USB or DC charger) ?

Your device freezed that is why it is stuck on the garmin screen. You need to first reset your garmin by holding the power on/off button for about 15 seconds, that way it will restart.
About the battery, when you get a new battery for your device, you need to charge it for about 3 hours before powering on, once you power on without charging it first, then it might kill the cells of the battery as they are lithium ion battery. What you have to do is to remove the battery, insert it back, then you plug it to a power source for about 3 hours, be sure that the battery is charging as the green light comes on as you plug it. If the green light does not come on, then you need to connect it to a computer using your USB cable, that way it will charge. Once it is charged for about 3hours, then you will be able to turn on your device. First reset, then charge battery. That should do the job for you.
Hope this information was helpful.

If you are charging your unit with the USB cable STOP - use only a wall plug. The unit will not charge using the USB cable. If you don't have the wall unit - try charging it with the car plug charger for 15 minutes. Just let the car charge it running or not. You will see it work. Once it is charge over half way - the rest will charge up. It is a problem Gamin is working on.

I've had this issue on my Nuvi 1300, where holding the power button for 10-15 seconds would restart the unit, but it would freeze at the "loading maps." part. I ended up plugging the unit into my PC, which started it for purposes of data transfer. I then disconnected it from the PC and it restarted properly.
Try that out and see if you have any better luck.

The Garmin Nuvi 855 uses a Lithium-ion battery. It is a very clean system and does not need priming as nickel-based batteries do. The 1st charge is no different to the 5th or the 50th charge.

In other words there is no memory effect with these batteries and it should be safe to charge it for as long as you like on the first charge. I would estimate 4 hours will give you a full charge if you wish to do this from the outset.

The video on the link below shows how to replace the battery in a Garmin Nuvi:

How To Change The Battery On A Garmin Nuvi 760

See also battery_repair.

Hold the off button (to the left) for 10 seconds... the system will restart and your garmin should work fine!