Since your battery is still not charged after over an hour of being on the charging dock, your battery is no longer holding a charge and needs to be replaced.
If the device does not detect the charging station when properly docked it is most likely due to a common issue with the charging pins. The charging pins on the LG G Watch easily become corroded when they come in contact with sweat or water. In this case the charging pins will need to be replaced in order for you to charge your LG G Watch