New York state's law relating to the warranty of habitability imposes upon the landlord the responsibility for maintaining a rented residential dwelling in habitable condition at all times.
That means, when a repair is necessary, the landlord will know about the condition when the tenant informs the landlord. An ordinary telephone call may be sufficient for most cases, but if your landlord is ignoring the call to repair then send the landlord written notice in the manner provided i the lease.
Although the landlord is required to make the repair, if the broken locks in the bathroom and bedroom doors was caused by the tenant's conduct, the landlord is free to charge the tenant for the cost of the repair. Most forms of standard lease allow the landlord to pass on to the tenant the cost of a repair caused by the tenant, as "additional rent" and to include the additional rent in a regular invoice for rent.
The answer provided to you is in the nature of general information. The general proposition being that you should try to avoid a bad outcome if you can.