Not a case at all. No body was injured, or had property damage. People get stuck in elevators every day, it sucks but it's not lawsuit worthy. Judges are not going to just hand over money to someone stuck in an elevator. The Fire Dept. was wrong, it's virtually impossible for modern elevators to free fall in an elevator shaft.
If you were smart you could find out the name of the company that serviced the elevator and dig for evidence that the landlord knew there was problems but didn't want to pay to fix it. You could also find out if the emergency button was knowingly left without an outside line to call for help. After that a lawyer may take your case but it would be tough to win. This ain't easy to do and since your asking 12 oz if you have a case I doubt you have the brains and ambition to pull it off.