I would start by checking the wiring connections between the charger and the battery. If neither the yellow or green lights ever come on, then you have a bad connection, or the charger has failed. If the battery has failed in such a way that it is an open circuit, you could have the same results, but this would not be a very common type of battery failure.
The charger is there to maintain the battery's state of charge. It should be left plugged in 24/7/365. If you are not using a sealed battery, the water level in the battery should be checked and adjusted every few months.