In his Beethoven: Biography of a Genius, Marek provides an insight into Beethoven as a boy:

The boy was looking out of the window, his head cradled in his hands.  His mien was serious, his glance rigid. Cäcilia Fischer came along the courtyard and saw him. “How are you, Ludwig?” she shouted up to him.  No answer. She said, “Foul weather seems to be with you.”  No answer. She said, “Well, no answer is an answer too.” Suddenly the boy exclaimed, “Oh, please, no, no, forgive me!  I was busy with such a beautiful, deep thought I couldn’t bear to be disturbed.”

This is one of the few vignettes which have survived.  It rings.  But how can one be sure?  Nor can any one anecdote flesh out the portrait of the boy Beethoven.  The boy, like the man, was contradictory – and contradictory were the impressions received by the people around him.

He was a merry boy, quite ready for pranks.  He played with the other children in the garden of the Palace.  He loved to be carried piggyback.  He sneaked into the hen house and stole some eggs.  Good-natured Frau Fischer caught him at it.  She called him a fox.  The fox steals eggs.  He said, “I am more of a music fox (Notenfuchs) than an egg fox.”

No, he was an exceptionally serious boy.  He was “shy and taciturn,” he was “enclosed in himself,” he was “peevish with people.”  He loved to turn the iron handle of the windows shutters and listen to the musical noise the handle produced. He was always maneuvering around the clavier and trying to improvise, to the annoyance of Johann, who said that he had first to learn how to play before he could compose.  His father took his little hand and guided the fingers in accompaniment of simple songs.  Then he set to work in earnest and stood before the clavier and wept.  He wept, probably because he could not master the instrument quickly enough.  He was ill cared for and often dirty.  Cäcilia said, “Why do you look dirty? You should make yourself proper:” He answered, “When I grow up, nobody will worry about it.”

Source:  Marek, George (1969) Beethoven: Biography of a Genius. London: William Kimber, p.39-40.