To "dawn on" also carries the implication of sudden light (think of the first moment of sunlight at dawn). Thus, "it dawned on me that . . . " doesn't mean that I arrived at a solution or answer gradually through working on a problem or question. Rather, it came to my mind suddenly (possibly after I had been thinking about it).
Example: John didn't return my phone call, and I couldn't imagine why. Then, it dawned on me that perhaps he had never received my message.