In the following clip, a doctor deals with a medical emergency on the telephone. The doctor is talking to a young man who found an elderly man (Mr Lindley) in the front room of his house slumped in his chair.
The young man is obviously shaken by what he found and the doctor does her best to calm the man who then proceeds to explain Mr Lindley's condition.
The young man uses the expression "Passed out" to mean that he thought that the elderly man was unconscious.
"There he was, slumped in his armchair, white as a sheet." refers to the condition that the young man found Mr Lindley in. 'Slumped' means sitting uncomfortably while 'white as a sheet' refers to the colour of his skin - unhealthy (sick) looking.