Hi there. My name is*****'m sorry that you're having this problem. I will do my best to help. When you plug it in to charge, do you see any lights or indicator that the device is charging?
Before we assume that the batteries are at fault, let's try to do a factory reset. Sometimes a software glitch causes these kinds of problems and a factory reset may correct that.
Note: A master reset will erase all favorites1 and will restore your device to the default factory settings. If you would like to back up your favorites to your computer, you can find instructions to do so here.
To perform a master reset on a nuvi 2407, 2408, 2507, 2508, 2707, 2708 series, Camper/RV 760, and zumo 590:
Another option to perform a master reset for these devices:
The device will automatically reset. Follow the on screen prompts to set your locale and then place your device in an area with a clear view of the sky until it acquires satellites.
Although the master reset will erase all saved favorites, any loaded custom points of interest will remain intact on the device.
Please give this a try and let me know how it works for you. If this solves the problem, would you mind taking a moment to rate my service? I'd really appreciate it! Without a rating I am not credited for my answer. If this doesn't solve the problem be sure to let me know so we can continue troubleshooting.