sat nav shows fully charged, whe unplugged it goes dead

Hi,

What is the make and model number of the device?

Even though it shows that it is fully charged doesn't mean that the battery can hold its charge or provide the necessary power to run the device.

Does it show that it is charging again if you reconnect it to a power source? Being fully charged it may but only for a very short time considering that it wasn't used for long, if at all, before the device turned off when on battery power only.

It may be that the battery needs to be replaced. Knowing the make and model number of the unit will help to find to find a replacement battery and also how to replace it.