You are not giving enough details. Why were your seats given away by Delta? And you state RCI made the air reservations....are you saying you booked an air/sea package with RCI? Specifically, what is RCI saying to you about their not being at fault? Did you use a travel agent or book directly with the cruise line? When you were not on the first flight, did you call your agent or the cruise line to update them on your flight status?
And for heaven's sake - you now know why it was really a bad idea to skip getting the insurance.