I have a Go720 in front of me.
As far as I remember the battery symbol only appears when you are running on battery power and the battery is running low.
But with it plugged into external power, the battery symbol disappears.
So I don't quite understand your question... I don't think I've ever seen the word "charging" appear below the battery symbol, but I don't think I've ever seen the battery symbol itself while charging either.
But I could be wrong.... It's fully charged at the moment so I'll leave it powered on for a couple of hours to run it down and check again.
More generally, if you haven't changed the battery yet, it's almost certainly dying by now on a machine of that age, so I would assume that's the problem.
If there was a problem with the USB connector then you wouldn't get the green light and it wouldn't work on external power.
I would go ahead and change it, but be extremely careful when prising the old battery off the circuit board. Use some sort of solvent to soften the glue, and don't try to lever it up in case you damage a tiny component, (it happens a lot).
