2 B's and one C. Do I still have a shot for Northwestern, Columbia, etc.?

It would be very unusual for someone to get into a highly competitive university from a community college. But, they might, if they have a 4.0 in the most rigorous courses offered, and fantastic recommendations along the line of, “This young person is clearly a late bloomer, but he has bloomed! He has found his passion, and is one of the brightest, most highly motivated students I have ever seen. He is clearly capable of performing at the most competitive university.”

Is that what you have?