Landlord won’t replace furnace

Landlord won’t replace furnace

Relavent location information - girlfriend and I are in Lake County, IL We've been dealing with a tempermental heater all winter. Three weeks ago, when it got bitter cold, we finally asked the landlady to see if her handyman father and the other people in the family who help him could repair it. They've replaced two parts on it now - one was the sensor and I'm not sure what the other was - but it still doesn't work properly. When it does heat up, it's nowhere near even the low settings on the thermostat we try to get it running and most mornings and nights, we can see our breath in most of the house. The only warm place is our master bedroom, since that has a space heater in it and a sheet over the doorway so the cat can come and go as he pleases. All of the cat's things are in the room. We highly suspect that the furnace needs to be completely replaced, but the landlady simply doesn't want to pay for that because she's going to be selling the house once our lease is up at the end of April and we're gone. No matter how often someone comes to tweak it, the warmth is gone in a couple hours (because of shitty insulation, but that's another story completely). Is there a way to legally compel her to replace the furnace? If it matters, I have asthma and spending more than 10 minutes in the barely-heated part of the house gives me terrible coughing and wheezing fits.
Plant ID?

Plant ID?

A few pics and a few questions

A few pics and a few questions

My apartment.

My apartment.

HOME GOODS

HOME GOODS

composter problems

composter problems

Bird Snacks

Bird Snacks