In the main battery chargers are switch mode in design, this means the whole device works in a circle, and any brake in the circle will cause it to fail, you can't as with old battery charges start at supply and go step by step with a meter, if it can be repaired likely done by replacing a module rather than a single component. In the main you can't repair them.
You don't say what battery type, with non lead acid one needs to be very careful, over charging a NiMh battery can cause it to explode, even with valve regulated lead acid you need to be careful. But at least with Lead Acid you can charge as three 12 volt batteries.
But even a simple car charger has safety built in which can stop you being able to charge a battery, mine will not work if battery voltage below 7.6 volts with a 12 volt battery, and auto shuts off at 16 volt, and putting a meter on the output will measure nothing until connected to a battery.
I selected a mower at random and read
Samsung 36V Lithium-ion cells ensure a reliable and long life battery performance
I would say you need to find some one with same mower, and try their battery in your charger, and your battery in their charger that is only real way to work out if battery or charger at fault.