Started A Lease On December 4th And Still Don’t Have Adequate Heat

I signed a lease to a unit on December 4th with the understanding that I would be getting a new HVAC by December 6th. It’s now December 19th, I have no HVAC still, and now the landlord is saying I won’t have it until after the new year, at least a month after the lease started. They are refusing to prorate or rewrite my lease to start in January until the HVAC is in because they gave me 2 space heaters, which the landlord says provides enough adequate heat. This is a 2 bedroom apartment in Kentucky in December, where our lows this weekend are going to be in the teens. For context, the owners of the property live in the LA area, so they probably don’t know what 15 degrees at night in December feels like.

This is on top of the multiple violations upon getting my keys and into the unit. When I walked into the unit on the 4th, there was no stove (included in rent), no smoke detectors, and the bathroom I was told had been completed on December 3rd was still a mess. I didn’t receive a stove until December 12th and the bathroom wasn’t completed until December 16th.

How do I go about bringing this to an attorney? Surely I have a case here, but is this worth bringing to a judge? I feel like I’ve been scammed and made a huge mistake.