Have you tried different chargers/cables in order to see if this behaviour persists? Also, have you tried forcing a restart of the device by pressing and holding the power-key and the volume up-key simultaneously for 10 to 15 seconds? Also, it is recommended that you use a charger that is plugged into a wall socket instead of using a computer (and USB cable) to charge your device. So try different power sources in order to see if the behaviour persists.
You should also make sure that the charger port is free from lint, dust and moisture. A blocked port can prevent the USB connector from fitting properly, and therefore prevent charging. Ensure that the USB port is completely dry, and gently remove any lint or dust using, for example, a wooden or plastic toothpick.
Also, If the battery is totally drained, it may take up to 30 minutes for your device to respond to the charging. During this time, the screen may remain completely dark, not showing the charging icon. Also note that it can take up to 4 hours for a completely drained battery to charge fully.