What to do if the landlord won't fix something?

Start with the lease first to see if it says anything helpful.  My guess would be that it says something about how to make the requests, etc., but there's a chance it has more helpful informaiton.  From there, you would want to look at Florida Statutes, Section 83.51 in conjuntion with 83.56.  Basically, if the landlord refuses to fix it, you provide a reasonable time to fix by written notice to fix it or you will withhold rent.  Do not just withhold the rent - you have to follow the procedure properly.  The procedure is dictated by the statutes so you might find it helpful to have an attorney do it for you, but there is a procedure.