Who is responsible for my injury from falling on ice in the parking lot where I work?

A month ago, as I was walking to my van in the parking lot of the building my employer rents space in, I slipped on ice and fell and slammed my face into the side of a car, then fell back onto my rear reaching out with my rt arm to break my fall. I ended up with a cut nose, black eye and bruised knee. I went to the Doctor the next day and x-rays were taken to make sure nothing was broken and that I did not have a concussion. Nothing was broken, only bruised via the X-rays. A few days after the fall, my right arm started to feel heavy and I had a sharp pain in my shoulder pain. Over the course of a few weeks, the pain and now numbness in my rt arm increased, and I had an MTI. It indicated that I have a torn rotator cuff and some bulging discs, believed to have been caused by my fall. Is the landlord responsible? The parking lot was not plowed the day before due to a malfunctioning security arm. But tenants cars drove in and packed down the 4+ inches of snow that fell the day before my fall. With the below zero temps, the parking lot became very icy. There was no salt thrown down that I could see. I called the property manager to file an accident report, but he said with the freezing cold temperatures, no one was at fault, and his liability carrier would say, "that's the kind of winter it’s been"! I work part time and when I don't work I don't get paid. I will be out of work for at least 10 days with my arm in a sling after the surgery. I have co-pays for Doctors visits, surgery and physical therapy. What can I do?