The Grey Lady had been known as Helena Ravenclaw in her life, the daughter of Rowena Ravenclaw, one of the Hogwarts Founders. Jealous of her mother's fame, and upset at the constant, unfavourable, comparisons between them, Rowena had stolen the diadem in the hopes of becoming less of a disappointment in the knowledge department.
Centuries later, she had been taken in by a boy with a silver tongue, Tom Riddle, who 'befouled' it and hid it away, reinforcing the ghostly woman's distrust of anything even slightly male.
They eventually found it, however, after taking the students on the pretence of a day-trip and scouring what Sirius termed 'the Butterbeer Room', but most referred to as the 'Room of Requirement'.
Again, no amount of knowledge stood up to the pressure and seven-hundred-plus degree heat of the furnace.
Meanwhile, no-one had been able to find a means of extracting the Horcrux from Harry, so they very, very reluctantly began looking into various forms of medically induced death.