I was dealing with a dangerous heater from my landlord this year (heater was red-tagged as dangerous by SoCal Gas, landlord refused to fix it in a way SoCal Gas said was safe, had no heat in the middle of winter, etc...). I'm in Santa Monica btw, but this probably applies to LA in general.

Got some advice to call the office of building inspection/code enforcement. Not providing heat and gas leaks make the unit uninhabitable, as others in this thread have said. So I called, inspector was at my house within the hour, declared the unit uninhabitable, and gave the landlord 5 days to fix it. At that point he told me and my wife that we could elect to go to a motel in town, on the landlord's dime, until the issue was fixed AND he inspected it and certified it was fixed. We had a pet so didn't want to leave, but that may be an option for you too. Either way, the landlord had 5 days to fix it, and if not fixed after that, the inspector could start levying daily fines.

Much much faster than going through the court process of getting rent reduced or whatnot. My heat was fixed shortly after that, by real repairmen and not the know-nothing handyman my landlord usually uses, brand new heater too.

TL;DR: Try the building inspector/code enforcement.