My GPA (Economics) at the moment is 3.7 but I have a terrible grade on Calculus II (C+)- the reason being that Calculus II clashed with another mandatory course of mine, and I couldn't attend most of the Calculus II lectures (furthermore, the Calc II Professor refused to accept my homework since I wasn't attending all the lectures, and all the grade weight fell on my final exam- most people who attended the lectures got super nice grades; also, the homework problems for that course were easy). On the other hand, I have perfect scores on all of my other Math and Statistics courses that did not have clashes. Furthermore, I will probably have my name on 4 papers by the time I graduate next year (please note that I have made significant contributions to the paper, and it's not just "some helping out on the research and my Profs. are too kind" thing). Apologies for the lengthy question.
If you don't get in to a great school it won't be because of a single grade. More likely it would be that there is so much competition from good candidates for very few actual positions.
In almost every place you apply people will look at your whole record and how you present it in the application materials. It is up to you to make your case. But you will need to make it well, showing that your background gives you the basis and your goals are appropriate and attainable.
It is possible that a few schools with a small staff and too many applicants may have to depend more on counting up chits than most, but it is possible to make your case even there.
But I wouldn't stress the low grade and the reasons for it initially. Give the explanation if asked, but don't put a spotlight on it.
Oh, and it probably isn't a good idea to self describe as a "dunce" in any application. But you know that, of course.
Let me say a few words here for the benefit of future readers. I worry more about an applicant with a perfect record than one with a few flaws. Nearly everyone will eventually reach a point in which things aren't easy anymore and have to deal with struggling through hard problems. If they have never experienced anything close to failure before then, when the going gets tough, they may just collapse. I've seen this happen.
I was lucky to get my struggles behind me early so learned how to work hard for success. One of my sisters totally outshone me in school, but found college a struggle as she hadn't learned that lesson. I was the turtle, but pulled ahead in the end. She wasn't lazy, like the hare in the story, but just hit a wall she couldn't seem to push through.