In South Dakota, if my insurance company denies my claim, do I have any rights?

Yes. In South Dakota, if your insurance company refuses to honor its contract and pay a valid claim, you have the right to bring a legal action for damages against the insurance company.  In addition to bringing a legal action for "breach of contract," you might be able to bring a "tort claim" asking for damages based upon the insurance company's "bad faith" handling of the claim.