Can my landlord take me to court for not paying all my rent?

I have been in my apartment since oct,2008 and when i moved in i tok pics of the place and made notice of the repairs. To this day no one has made repairs to my apartment. I even called the city inspector, and to mu knowledge the owners have 14 dys to start on the repairs. It's is now 2 months later and all they have fixed is 34 sockets and they just changed the cover on them, the wiring was not checked. Not to mention the heat is supposed to be included, but the heat is so insufficient, that i had to let my kids live with thier grandmother because the apartment was just that cold. My radiators come on because they are on a timer, but they dont stay on l;ong enough to warm up the apartment before they shut off. I have sent repair notices, taken pictures OFTEN, and still, they want the rent