There are numerous options for obtaining repairs in a NYC apartment, and for obtaining compensation for lack of repairs. They all have advantages and disadvantages. The best way to figure out which one to choose is to have a consultation with a lawyer.
Generally, every residential tenancy in NY (in buildings of three or more units) is covered by a statutory warranty of habitability. A landlord breaches the warranty by failing to make repairs. The measure of damages is not the full amount of the rent. Rather, it is the difference between what you paid and the reasonable value of what it was worth. There is some precedent for recovering your expenses (i.e., eating out, increased electrical costs), but this legal point is not completely settled. You can sue for the diminished value of the apartment and may also recover your expenses, if you decide against the other options outlined below.
Since you went to court and got an agreement, you may be in a position to ask the court to hold the landlord in contempt of court for failing to repair as agreed. You can do this only if the agreement was in the form of a stipulation that was "so ordered" by the judge, and you haven't waited too long (e.g, a year) to come back to court. The damages caused by the landlord's breach of the agreement can be recovered in contempt proceedings, but not the damages from before the agreement was signed. Contempt proceedings are effective but they are highly technical, and usually require a lawyer.
You can withhold some or all of the rent, but if you do, you should expect to be taken to court in an eviction proceeding. The landlord's breach of the warranty of habitability and of his agreement to make repairs are defenses that result in the rent being reduced, or "abated." Tenants who are sued for nonpayment, however, will find their names on blacklisting databases, which may impede their ability to get another apartment.
If you are in a rent stabilized apartment, you can file a complaint of "decreased services," which will result in an order requiring the repair, reducing the rent, and freezing it at the reduced level until the repair is made. This is often the most hassle-free method of proceeding, but it often involves the landlord being given multiple additional opportunities to make repairs.
If there is a solid paper trail establishing a landlord's refusal to make repairs, some repair issues can be handled by simply making the repairs yourself and, if you choose, deducting the cost from the rent. Stove repairs are not a good candidate for this, though, since the work arguably requires a permit and only the landlord can get one, since it must be performed by a licensed plumber, and since these requirements give the landlord ammunition for bringing an eviction proceeding.