Where to begin your story?

Deciding where to start the story is a dilemma for many writers. 
Do you begin at the beginning? The middle? or even the end?

Adrienne told us a story to illustrate how where you start sets the tone.

It was John and Mary's twenty-fifth wedding anniversary and John had booked a table at Mary's favourite restaurant. 
They had a wonderful romantic meal, they drank champagne, held hands  and talked about everything they had done together. The candle flickered and a fairy appeared.
'Mary and John, you have had a perfect marriage, caring for each other in sickness and when times were rough. You are an example and we would like to reward you. You can have anything you want.'
'You go first, love.' John smiled at Mary.
'Anything?' 
'Yes.' The fairy fluttered closer to her.
'I'd like to go on a five star world cruise.'
The fairy waved her wand and two tickets landed on Mary's plate. Her eyes shone with happiness.
The fairy turned to John. 'Your turn.'
'I am happy with the cruise. I do not need anything else.'
Mary frowned at her husband. 'John, you must ask for something. It would be rude not to.'
'Anything John. What is your hearts desire?' The fairy held up her wand.
John took a deep breath. 'I'd like to be married to a woman thirty years younger than me.'
Mary gasped as the fairy waved her wand.
An eighty-seven year old man sat opposite Mary.


After our laughs of surprise died away she began another story -

John sat on the dock in his wheelchair, a blanket tucked around his legs. Tears blurred the sight of a cruise ship pulling out of the harbour.

Point made.

Same story, different beginning.
The first version is funny, the second poignant.

In a Podcast - Writing Excuses- one of the authors said he would generally discard the first three chapters of his first draft- they were the warm up to the story. 

I am rewriting The Finder, beginning in a different point in the story.

Could you start your story in a more dynamic place? Would it change the tone?