Unfortunately for you, your reasoning is correct up until point 7. The plane does not take off, because there is no force imbalance. There is simply no net force in the vertical direction (a.k.a. lift), so the plane does not move upwards. That is the job of wings, alerons, flaps and slats: transform the horizontal motion of air passing over them into a vertical force which balances gravity, or exceeds it slightly (in which case Newton's Second Law stipulates an accelaration in the upward direction), or is slightly smaller (in which case there is accelaration in the downward direction).
That is also why loss of lift results in such catastrophic accidents. The plane still has lots of horizontal velocity relative to the air, but the areas which are responsible for lift don't do their job any more. The plane is then literally a brick due to impact on the ground within (I think) at most two or three minutes.
Later edit: Ack, ick, phooey. I never got the hang of the differences in torques in freely rotating bodies, or those which were powered to do so, when both are presented with a solid surface. Of course I am completely and utterly WRONG: The plane WILL take off. It's the same as when an airplane would be taking off from a completely iced-over runway. The wheels would just slip over the ice (and in fact, nearly stand still) so you'd lack the ability to steer unless you throttle the engines separately. But take off you will. The morale of the story: don't put a soapbox race car with JAT engine on those rolls used to test car performance in the lab, because you'll create one heck of a hole in the wall...
