Laura Gerstel, 20, had spent the day before her death happily Christmas shopping with her mother, but hours later her friends discovered her body hanging by a red ribbon.
Just before she was found Miss Gerstel had updated her status on the social networking website to read "Laura is thinking 'if only...'".
She also left a note indicating that she thought she was overweight, and said she did not wish "to live this way", an inquest in York was told.
Antony Gerstel, Miss Gerstel's father, said that she had begun self-harming from the age of 12, and was had suffered from the eating disorder bulimia at 16.
She had briefly been referred to a psychiatric hospital after her parents had found cuts on her wrists and legs.
In a statement Mr Gerstel, from North Berwick in Scotland, said: "She would not let us help her. But when she was at university she sent us happy texts and sounded fine."
The student, who was in her third-year of a Biochemistry degree at the University of York, had spent the day shopping with her mother on November 25 last year.
But in the early hours of the following morning, after her mother returned home to Scotland, Miss Gerstel's body was found by her housemates at 4am.
One, Emma Wellard, said: "I came out of my room and saw Laura suspended from a red ribbon tied to the bannister. My housemate phoned for an ambulance.
"I had known her for two years. She suffered from bulimia, took anti-depressants and did cut herself."
Miss Gerstel's poignant final Facebook message was posted at 2.46am.
Coroner Donald Coverdale dismissed a verdict of suicide because she had drunk the equivalent of two-and-a-half pints the previous evening. Mr Gerstel said in his statement that his daughter "became compulsive" when she drank.
Returning an open verdict, he said: "This is a very sad story. Laura had suffered from a number of medical and psychiatric difficulties, and unfortunately had harmed herself in the past by cutting herself.
"I am not aware of any previous attempts to take her own life. The note she left referring to her thoughts and feelings that she was overweight connects to her psychiatric difficulties.
"The level of alcohol she had consumed may well have impacted on her judgement. Because of the uncertainty about her motives and the state of her mind due to the alcohol, I am going to record an open verdict. I'm afraid we shall never know what was in Laura's mind."
None of Miss Gerstel's family were present at the inquest.
