In Game of Thrones, did Cersei Lannister not find anyone else in the entire King's Landing to satisfy her desires? At least someone other than her own brother to be the father of all her children? When did a lantern go off in her head that got her thinking that doing Jaime was a good idea? Yes, even though she tells Ned that since they are twin siblings, they are somehow predestined for each other, but still....Why Jaime and Lancel Lannister later, just because he resembles Jaime a bit.
Did she not find ANYONE else in the entire King's Landing to satisfy her desires?
Jaime and Cersei have been having a physical relationship long before either of them went to King's Landing, as is revealed in Jaime's third chapter of A Storm of Swords:
He could never bear to be long apart from his twin. Even as children, they would creep into each other’s beds and sleep with their arms entwined. Even in the womb. Long before his sister’s flowering or the advent of his own manhood, they had seen mares and stallions in the fields and dogs and bitches in the kennels and played at doing the same. Once their mother’s maid had caught them at it... he did not recall just what they had been doing, but whatever it was had horrified Lady Joanna. She’d sent the maid away, moved Jaime’s bedchamber to the other side of Casterly Rock, set a guard outside Cersei’s, and told them that they must never do that again or she would have no choice but to tell their lord father. They need not have feared, though. It was not long after that she died birthing Tyrion. Jaime barely remembered what his mother had looked like.
A similar event is mentioned in the show, however that does not make it clear how old they were at the time. Cersei is very much willing to sleep with other people if she cannot be with Jaime, as we hear of her having sex with Lancel Lannister while Jaime is captured by the Starks.
So to answer your second question:
When did a lantern go off in her head that got her thinking that doing Jaime was a good idea ?
Some time before they both hit puberty (10-12) at least.
The most recent book, A Dance with Dragons, also has Cersei admit
That she was also is sleeping with Osmund Kettleblack and his brothers: Osfryd and Osney. Tyrion told Jaime she had been sleeping with Osmund at the end of A Storm of Swords, but as I recall this is just speculation.
However these characters have not been seen in the show so it will likely be cut out.