Registering your boat in Florida can be a real PITA. I had built a small sailboat several years ago. No license is required for sail boats or manual powered boats. I decided to tiuse a wee little 2 HP motor on some ocassions. That means that I had to register the boat and get a boat license number. Sheeesh!!!!!
First, is that you have to get a Florida Wildlife officer to examine the boat and then go through a bunch of hogwash administrative stuff and end up with no reply or other resolution. Weeks went by and I had exhausted my considerable patience with the department of motor vehicles and the FWC who are for some reason involved. Try to call the DMV in Tallahassee and good luck with that. No way you can get to a human at that number. To hell with all that then, I will appeal to a higher authority. (No not God, but a politician) I resorted to contacting my state representative and my state senator. Wow! that really worked well. After a short period of time I got a phone call from the office of the politician and things got rolling after that.
Yours is a similar but not identical dilemma When you finally get an audience with the district tax collector you will need to produce a bill of sale or some other evidence of purchase so that the state can charge you sales tax on the purchase price. If you got the boat for free or as a gift..........no telling what the outcome of the tax assessment. After that you get to pay for a license that will cost you about $40 per year, depending on the size of the boat. Big boats cost more for a license.
I feel for you, and good luck with whatever resolution you may find. Meanwhile do not use any kind of mechanical power on the boat. A FWC officer will bust your chops to the tune of a considerable cash fine if you do not have the license numbers on your boat as well as all the safety gear such as PFDs, fire extinguishers, signalling devices and all that jazz. It is not easy to be a law abiding citizen when the price is high and the administrative mess has laid a curse on your good intentions.