My position is the same as TJ's, and I would place the point at which sins can be actively committed some time around the shift from the first to the second growth stage in mid-childhood (although I do think that the culpability is at least somewhat diminished until some point in adolescence, insofar as such things are quantifiable).
What about 'responsibility' into adulthood? At what point in life is any person completely endowed with the faculties to make morally correct or incorrect choices? Whom is the standard on which you can measure whether other people meet or fail to meet culpability? Is adulthood not a learning curve in itself, or are you expected to know the nuances of what is moral and what is sin as soon as you are an adult, however you choose to define it?
In short, how on earth can anyone with any honesty say that you can quantify the point at which 'sin kicks in' when no other moral or ethical standard is complete and absolute at the onset adulthood and ultimately is affected by experience and social interaction? What is galling is that you have tried to be objective in utilising child psychology yet you've ultimately bastardised it.