Rental has terrible carpeting flooring and Landlord won't fix it

[Francesco Adriatico]

Hello everyone, 

Last month, I started renting a semi-basement in a building in New Jersey. 
When I moved in, the apartment heating was not working and I had to fight with the landlord and threaten him to not pay rent in order to get extra baseboard heaters in the apt. 

The apartment has however many other problems. The blinds in the windows are all broken (in not missing), the windows do not lock (I do have some "cage" alike protectors outside of the windows though being them at street level) and the carpeting flooring is in terrible terrible shape (heavily and terribly stained). 

During Christmas, I have been traveling and the landlord promised me he would have cleaned the carpet while I was gone. Two weeks after I come back in the apartment and the carpet is still stained. He told me he had someone try to clean it but that they couldn't do much. 

I would like to know if I can demand flooring to be fixed or not (along with all the other issues), or if at this point is a matter of ethics more than law. When I asked for the heating to be repaired I knew I had the law on my side... But this time I am not sure if it so, since in my lease there is written that I have inspected the apartment upon signing. 

Thanks in advance!