The device is switched on while you charge it? I had the same problem with the jornada 680, I had only to switch it off and re-attach the charger... It could be a died battery, or a bad non-original charger too...
There's your problem right there. That won't provide enough power to charge the device while it is in use. The stock 720 charger provides 12 V at 2.5 amps.