"I didn't operate a business or farm in Florida that has tangible personal property, but I have a business..."
You would only need to consider filing Florida Form DR-405 with your county property appraiser if you had tangible personal property that you used in connection with your business.
See http://floridarevenue.com/dor/property/tpp/
Also check your county property appraiser's web site --> http://floridarevenue.com/dor/property/appraisers.html
