Dear Lovenut,
So the central component here is whether you have a warantee or not. I'm inclined to believe given the cars age, and that all cars purchased from a main dealer brand new have at least 3 years/36,000 miles warantee that you do. Unless this problem has occured before and had to be fixed by the dealer then it is absolutely their responsability and legal obligation to fix it. Its difficult to give an accurate quote for repair if you do not have a warantee, as every workshop is different, though main dealers will always be the most expensive and not neccessarily the most skilled. So if you do have a warantee on the car (should be in your paperwork, and the dealer is obligated to tell you if you call them) then NEVER repair yourself or have another workshop other than a maindealer work on the car, as not only will you be paying extra for parts and in some cases labour but it will certainly invalidate the warantee if work is carried out on the car by anyone but a main dealer authorised to reapair your model of a car. So from the information you provide I reiterate I'm fairly certain you have at least a years warantee left, but do check it out with the main dealer.
Good luck
RWJ