Even when Mr. Hastert told Individual A, as investigators listened in, that he needed more time to come up with more money, Individual A “did not make any threats” and even “expressed understanding,” the prosecutors said. At another point, Individual A seemed agreeable, even empathetic, suggesting that they settle on smaller amounts and keep the payments as a “private, personal matter.” Individual A even pushed Mr. Hastert to tell his wife about the payment agreement, and suggested that an outside lawyer or confidante might be called in.

Of the abuse of Individual A, prosecutors said there was “no ambiguity.”

Prosecutors said the motel incident had happened during a trip to a wrestling camp, in which several other boys shared a room but where Individual A and Mr. Hastert spent the night together. Individual A told prosecutors he did not know why Mr. Hastert had singled him out.

The court filing says Mr. Hastert had the boy strip naked and lay on a bed under the guise of treating a groin pull, but it “became clear to Individual A that defendant was not touching him in a therapeutic manner to address a wrestling injury but was touching him in an inappropriate sexual way.” The boy then ran across the room, confused and embarrassed, before Mr. Hastert asked him to get onto Mr. Hastert’s back and to give the coach a massage. “Defendant lay on the bed in only his underwear, and Individual A gave him a back massage,” the prosecutors said. “They then went to sleep in the same bed.”

When Mr. Hastert was charged last year, the accusations rattled the town of Yorkville, Ill., about an hour west of here. Mr. Hastert, a Republican who served as House speaker from 1999 to 2007, was regarded as a hero by many in Yorkville, where he had taught high school. But prosecutors said Mr. Hastert’s life had been “marred by stunning hypocrisy.”

They alluded to a fifth boy from Mr. Hastert’s days in Yorkville who recalled Coach Hastert brushing against his genitals during a massage at one point. But he said he was unsure whether the contact was intentional though he found it “very weird.”

Of the boys, prosecutors said: “He made them feel alone, ashamed, guilty and devoid of dignity. While defendant achieved great success, reaping all the benefits that went with it, these boys struggled, and all are still struggling now with what defendant did to them.”