Prior to the fall, none of Bran's Warging nor Greensight abilities had manifested themselves. The most he had shown was a stronger than usual affinity with his (then unnamed) direwolf, which is an ability he shared with the rest of his siblings. After his fall, those abilities started to show up.
The warging ability was not something unique to him. The rest of his siblings have shown some grasp of it, but none to the extent of Bran's warging prowess. This could be because Bran is naturally stronger, or that his disability gave him more incentive to project it.
The Greensight, however, is something he enjoys alone and only manifests after he falls. During his coma he has visions of the Three Eyed Crow. Spoilers follow:
It is revealed by the end of Season 4 and the sixth book A Dance with Dragons that the visions were sent to Bran by a mysterious person with tremendous powers who calls himself the Three Eyed Crow. His real name is not revealed in the TV series, but it is in the books.
Now, why did the TEC wait until Bran was in a coma to reach out to him? We still don't know. Perhaps during his coma, Bran was more receptive to the TEC's visions, and it is quite possible that it was through these very visions that Bran's latent powers were awakened. In the books the TEC picks Bran's forehead in order to open his third eye, and it is then that Bran awakens from his coma.