Anne-Marie Ellement, who died two years later, was stationed in Germany at the time of the alleged attack in 2009.
The 30-year-old from Bournemouth, Dorset, was found dead at Bulford Barracks in Wiltshire in October 2011.
Former corporals Thomas Fulton, 28, and Jeremy Jones, 28, who have since left the Army, both deny rape.
A panel of civilian and senior military officers heard Cpl Ellement was serving with the Royal Military Police in Germany at the time.
They were told she bumped into the two accused in the corporals' mess, where they all drank heavily and left together.
Prosecuting, Sarah Whitehouse QC told the court both soldiers admitted sexual activity took place, but they insisted Cpl Ellement fully consented.
She said Cpl Ellement was found in the early hours on 20 November in a corridor in the Army quarters where she lived, and was naked apart from a long cardigan.
Ms Whitehouse said: "She appeared to be extremely drunk. She was struggling to keep her balance. Her feet were muddy and she was crying."
Cpl Jones later said the three had all undressed in his room and both he and Cpl Fulton had consensual sex with Cpl Ellement, the court heard.
He described them all as "giggling and being silly" throughout.
Cpl Ellement said in her video interview she had no recollection of sex with Jones.
Another colleague, Cpl Kelly Broadhurst, came to help Cpl Ellement and heard her say: "I didn't want it. He tried to have sex with me".
"She said he had sex with her and she said 'stop' but he carried on for 10 minutes," Ms Whitehouse said.
Cpl Fulton and Cpl Jones were arrested later that morning and were interviewed.
Cpl Fulton declined to comment, while Cpl Jones insisted both men had consensual sex with Cpl Ellement.
Speaking of Cpl Ellement's death, Ms Whitehouse said the "circumstances of that sad event are not relevant" to the court's task.
The trial continues.
An "extremely drunk" army corporal was raped by two other soldiers after a night drinking together, a military court in Wiltshire has heard.