Can your computer see the device when it's connected?
If the battery is very flat, it may well take some time to charge fully enough to boot up the screen and operating systems. Similarly, it might need a kickstart. Try pushing, holding the power button depressed and then releasing it. This assumes of course that you are successfully charging the device.
Try disconnecting the battery and then carefully reconnecting it, just in case some damp / corrosion has got into the contacts.
Some external chargers are seen by the device as a computer, which might not always allow charging to take place. Connecting the device to a computer will (most often) allow charging and computer operation at the same time. For instance, I have updated the software / maps on very flat (zero power) Nav V's and charged the devices at the same time from my Mac. I sometimes have to hold the power button depressed in order to boot them up afterwards, as described above.
PS Try the GPS section too.