By design, if you are charging the unit while it is turned on, the charging indicator will not light up. This does not imply that the unit is not charging.
To make the charging indicator visible and verify that the battery is indeed charging up, turn the unit off.
NOTE: Turning off the unit will also decrease the charging time.
In the event that the charging indicator is not lighting up when the unit is in turned off and connected to the AC power supply, press the reset button at the back side of the unit and try again.