LG cell phone charger- Look over it and check for any tears or other damage to the device. If you see any, the charging problem is most likely with the charger and not the cell phone. Replace the charger and check whether the phone is able to power the battery back up again.
Spray compressed air into the mini-USB port. This expels dust and other debris that clogs the charger port, preventing it from connecting to the charger or USB cable.
Take your LG cell phone to your wireless service provider. It is possible the battery is dead, in which case you will need a replacement.