f I connect a charger, to a laptop , must the laptop start if battery is flat ( or disconnected) and charging circuit is damaged? Or the working charging circuit is necessary for a laptop to start?
No, the battery doesn't have to be flat. The charging circuit in the laptop will only charge the battery, if it needs to be charged. The laptop will be happy connected to the mains power supply, whether the battery is fully charged, or flat.
If there is a fault with the charging circuit, the battery will most likely not charge. There is a risk it could overcharge, in which case, the battery should have a protection circuit, to prevent fire and leakage. Some laptops won't work without a battery, which indicates the battery charging circuitary is part of the internal power supply. If you suspect the laptop's internal battery charging circuitary is faulty, you shouldn't attempt to charge the battery with it.