if the head gasket failed in a serious way, compression would be way down rather than "It is very hard for the starter to turn the motor over unless the battery is fully charged." That implies the opposite of a blown head gasket - high compression. But why would anyone trouble shoot a starter problem using an under-charged or worn out battery? The first step would be to test the battery before and after charging, clean the terminals and ground etc..
The head gasket could be a little leaky in the scenario above where it might cause high breather pressure if the engine head has an oil supply or return passage. But say it is an L head engine like an old push behind Murray might be, then there is no place the combustion gasses can escape to except out.
Of course since you haven't listed engine model information it leaves everyone trying to read someone else's mind. My skills in doing that are a bit off lately. How are yours?