Sometimes, people might not be as unconnected as you think. To give you an example from the urban environment, I've seen download kiosks where somebody with a computer will download music videos and songs and then install them on memory cards for squatters, street vendors (living next to/in their stalls) and others that might nominally be seen as unconnected.
In other instances, "connection to the Internet" might look very different than one would assume. For many of the rural residents of the 4.3 bn you mention, the Internet is meaningless unless there are the types of applications that these people are interested in and/or in need of. They are not blessed with the potential for leisurely media consumption nor are they skilled to access information and / or modalities of use provided primarily for literate audiences.
I hope when you speak of connecting the unconnected you are not thinking of providing pipes of bandwidth or even new consumer devices? That has been tried and is clearly not the way forward. Rather building services that specifically target the needs as well as limitations faced by "the unconnected" seem a much more viable proposition - perhaps working with (and not reinventing or innovating around) the modalities already being developed, such as the "download kiosks" mentioned above.
First and foremost, though, I hope you are spending plenty of time with the unconnected when developing this idea.