Tow Company Denied Having My Car And Now Wants Me To Pay For Several Weeks Of Them Storing It

My car was towed from a hospital garage several weeks ago. There are signs warning of this if the car is left overnight, but the signs do not specify the tow company or lot it will be towed to (also I stayed overnight because I was hospitalized so it seems a strange policy...).

When I got out of the hospital my car was missing so I asked the parking attendants who could have towed it assuming it wasn't stolen as I have a Kia Soul. The parking garage directed me to call the police as a report would have been filed with them if the car was towed. The police gave me the number of the tow company, but when I called the tow company they said they did not have the car in their system after checking using the license plate number.

A couple weeks go by as I'm redirected to different tow companys, impound lots, nonemergency police phone numbers that no one answers, etc. I get the same tow company info a couple more times, but each time I call they state they don't have the car. I finally go in person to a police station and stay there until they can assure me that the report was filed with that tow company. For whatever reason when I call them for the 4th? time, the person who picks up the phone again states they don't have the car, but maybe it's with their OTHER LOCATION.

The police info was that the car was towed to their north branch, but turns out the south branch has it. When I call the south branch, they verify they have my car, but since this process has taken ~2 weeks, it'll cost close to $2,000 to have my car released. Is there anything I can do? That's a lot of money for me, especially after the hospital.