The first real evidence Corran has of his Jedi heritage is when he is escaping from Lusankya. He enters a closed-off portion of the Jedi exhibit in the museum on Coruscant, where he finds an display dedicated to Nejaa Halcyon. It is here he learns that Nejaa is the man on his medallion, and it is hear that he first sees his father as a Jedi apprentice. It is in this room that he also first uses a lightsaber in combat, having acquired Nejaa's.
Interesting note here: Corran at first positively identifies the boy as his father, and even notes how the boy somewhat looks like him personally, but then tells himself that the hologram had to have been wrong and he had to have looked at it wrong. In short, he flat out denies what his eyes are seeing and his mind has deduced.
At the reception following the awards ceremony at the end of The Krytos Trap, Luke Skywalker tells Corran about his Jedi heritage. Corran does everything in his power to deny it, telling Luke he has to be wrong, the lightsaber does not belong to him, and his grandfather is Rostek Horn. He is forced to accept the truth, however, in the light of Luke's facts and deductions.
Luke offers Corran the chance to train as a Jedi Knight. With barely a pause, Corran declines the offer, citing his promise to free the Lusankya prisoners. He does keep the lightsaber, however.
Privately, however, he may have had some regrets over that decision, and there may have been more factors behind it. He acknowledges that he is from a line of Jedi, but also goes on about how it's not the whole truth because it's not the truth he grew up with.
At this stage, personal obligations and promises are more important to him than the galaxy as a whole. He thinks this in connection with the Lusankya prisoners, but knowing Corran, there is probably more to this than that one thing.
He chooses to wear his lightsaber, but at first he feels awkward in doing so. His perception of lightsabers was that they were more of a genteel weapon worn by either Jedi or those who weren't brave enough to wear a blaster or another, more efficient weapon. He didn't like wearing it because of the wimpy connection, but did still feel right wearing it because it was a part of his heritage and because he felt it would make Rostek proud.
After rejecting Luke's offer to train, Luke sent Corran articles and reading selections on the Jedi. Included in those were Jedi relaxation techniques, basic lightsaber maintenance and fighting styles, and stories of Jedi in law enforcement roles and being viruous and just.
After reading the material that Luke sent, Corran began to second-guess himself, not knowing whether anything he was feeling at a given moment was normal or if it was instead a manifestation of his Jedi heritage. This dilemma plagued him until he finally decided to undergo Jedi training.
Corran's first active attempt to use the Force fails utterly when he tries to influence a stormtrooper's mind on Thyferra. He ends up getting into a fight that culminates in injuries that would have been fatal if not for bacta being available.
Corran had learned at an early age to trust his feelings, and had always given them weight when making his decisions, but he had never questioned where those feelings were coming from until finding out about his Jedi heritage. The few times Corran didn't trust his feelings usually ended up in disaster for him.
One of Corran's fears about knowing where his feelings are coming from is that if he says anything one way or the other, his friends will take what he says as the truth because of the Force. He is afraid that they will do so and that Corran will be wrong due to his ignorance about the Force, and that his friends will pay the price for that ignorance.
Corran claims he doesn't feel betrayed that Hal never told him about their heritage, but only bothered that his father had to have been very proud of it, but was never able to speak of it. He understands that the reason he was never told was because Hal was keeping him safe from the Jedi Hunters. He also realizes that his father did do his best to circumspectly raise him according to the Jedi code and encourage some Jedi behavior in him by telling him to trust his hunches. He believes that Hal was only waiting for the Emperor to die before telling him everything.
Corran discovered that Whistler is carrying a holographic message of Hal Horn. Hal uploaded a message for Corran discussing their Jedi heritage in the event of Hal's untimely death. Whistler was to play it when Corran asked for it and could provide the proper encryption key. He is not positive his father had foreseen the reemergence of the Jedi Knights, but he believes the message will urge him to at least learn more about his heritage, if not outright telling him to undergo Jedi training.
Corran chooses not to listen to the message from his father for a few reasons. He is afraid that his father will tell him to pursue Jedi training, and he doesn't want to do that at the moment. He cites prior obligations to the Lusankya prisoners and to Rogue squadron. He also is afraid that training to be a Jedi would force him to give up Mirax, or at least leave her for a long time, both things he does not want to do. He also sees the message as the last thing his father ever left for him, and he doesn't want to lose that idea. He sees it as a sign of his father's trust that Hal left it up to him when, if ever, he would play the message, and he thinks putting it off will make the gift last longer.
During the briefing before Tal'dira was killed, Corran was the only one who noticed that Tal'dira did not even seem to be aware that a joke had been made involving him. This probably had nothing to do with the Force and was simply Corran looking over to gauge Tal'dira's reaction to the joke. Corran may have been alerted consciously to something perhaps being wrong with Tal'dira by this, though. Corran did receive a warning through the Force right before Tal'dira fired on Wedge, giving Corran a chance to cry out a warning to Wedge in just enough time for Wedge to maneuver himself enough not to be killed. I'm sure this warning would have come without Corran being alerted to something being up with Tal'dira, but his awareness of Tal'dira's offness may have aided him in knowing of what exactly the Force was warning him.
Corran was able to get through to Tal'dira by saying, "Tal'dira, this isn't honorable. You shot him in the back." (Solo Command, p. 126) It is unknown if the Force guided him to this key to Tal'dira's character or if Corran had known him well enough to be able to logically come to that conclusion. Either way, Corran did have to kill him.
Later on, in another battle, Corran does his typical maneuver where he cuts power to his engines just long enough for the enemy to shoot out ahead of him so he can kill him. Flying in the same battle is Tyria Sarkin, who is in the flow of the Force. She can sense the intent of everyone around her before they actually do something, but she could not pick up on Corran's intent to execute this maneuver. When she asks why, Myn tells her it was experience. Could Corran be experienced enough to just be able to do this maneuver without even thinking about it first, or can he somehow (probably unknowingly at this point) shield his mind from weak Force probes?
Corran was the one to know that every other pilot in the ersatz Fel's squadron was a robot because of the Force. He started out by just thinking tactically like a pilot, but then just got this feeling through the Force that turned his gut cold. That's when he knew that some of the TIEs did not have living pilots.