Whether or not you have a claim under the lemon law depends on additional facts: did you buy it new or used, what the reason for the breakdown was, whether you followed the lemon law procedure through the Florida Attorney General's office, etc. However, you may have other claims if they misrepresented the condition of the vehicle. One thing to be aware of: this depends in part on the exact terms of the purchase contract and related documents. Beware the "fine print"! Good luck to you.
You do have rights! If they misrepresented to you the condition of the vehicle. If they informed you that the vehicle was in excellent condition, or was not in an accident, or any other material misrepresentations, you may have a consumer fraud claim. This is not a lemon law claim, but still would allow you to attempt to unwind the deal and get you your money back or a diminution in value. I would run a carfax report to determine the history of the car as a first step.
Additionally, if you purchased the vehicle with a warranty, whether it be a week, month or year, that creates certain express warranties and warranties implied by law. If you have taken the vehicle back to the dealership to make repairs you have taken the firs steps. This would be a lemon law claim for breach of the warranty.