Upon word that your cousin Edward has died, you send to the witan your offer to be their king: the promise Edward gave to make you his heir is rehearsed and considered. Their reply is polite but brief: "The English will have an Englishman for their king. We have chosen Gyrth, the brother of the man you murdered."
Well, that is the guantlet thrown down all righty. But what can you do? All your excuses to justify your right of rule in England fall in the end on deaf ears: Gyrth is a legally chosen king. You have nothing but the promise of a dead man to you. The pope does not want you invading a Christian land, whose king is willing to cooperate with church reforms there.
When word comes across the Channel, that Gyrth's army has inflicted a complete defeat upon Norse invaders under the command of their king Harald Hardrada, and killed him in the bargain, you must face the inevitable and let the conquest of England go. Still, it eats at you: the kingdom should be yours. You remain on your side of the Channel, at war with Bretons and others from time to time, but accomplishing nothing of further note. History remembers you as a powerful duke and a competent warrior, but "Conqueror" is not an epithet that survives your living memory.