A Florida lawyer would be best to answer this question. I can answer in general from what would happen in Illinois. Until a deed is transferred the persons on the deed are liable for the homeowners dues. Laches is usually not a winning argument in most circumstances. If you were on the deed at the time of the HOA dues then likely you are liable for the debt.
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You will be liable for all the dyes levied against the property during the time you were a owner and listed on title. However, after your names was removed from title, you will not be liable for any dues after that date. As far as statute of limitations, the claim for the delinquent dues is usually considered a contractual claim because it is governed by the Association's declaration and governing documents. Check with an attorney in Florida to see what the statute of limitations is on a claim based under contract. Usually, a contractual claim will not expire within only two or three years though.
Unfortunately, under Florida law, you are probably personally liable for both the HOA dues on the property while you were the owner and for those that accrued before you owned the property. If you received title insurance when you bought the property, the past HOA dues should have been collected at the closing. You may be able to recover these from the title agent or the title insurer. It will probably be difficult for you to escape liability for the time that you were an owner of the property. If you are unsure of your rights and responsibilities, you should consult an experienced real estate lawyer in your area.
Disclaimer: This answer is provided for informational purposes only, does not constitute legal advice, and does not create an attorney-client relationship. Actual legal advice can only be provided after completing a comprehensive consultation in which all of the relevant facts are discussed and reviewed.