It all began with a simple decision made by Albus Dumbledore several weeks after he had left Harry to his relatives. Instead of simply assuming the goodness of all relatives who would surely wish to help a poor, orphaned nephew, Dumbledore found himself reflecting upon the rumoured ill-will between Lily and her muggle sister. Deciding that he wasn't one to take a chance on this at all, he owled Gringotts late at night with an order to compensate the Dursleys for an amount of three hundred galleons per month straight from his own account. He could always have the Ministry compensate him as well, as they would be just delighted to inform the public that they were providing for the orphaned Boy Who Lived. Having decided that on this occasion that satisfying such pecuniary self interest would likely have a more beneficial than malevolent effect, Dumbledore wrote the letter informing the Dursleys that they could expect such regular payments to continue so long as they took good care of Harry.
This simple change of heart by Dumbledore had a profound effect on the upbringing of the Boy Who Lived who passed a much more regular childhood. While Harry still noticed that his relatives resented and often shunned his presence, he took it well understanding that they were not his parents, and therefore could never be exactly compelled to shower him with affection, even though he knew they were getting paid for it from a wealthy benefactor that he had overheard the Dursleys telling Marjorie Dursley. But he never lacked any food to eat, he was never punished unless he really felt he deserved it by playing a prank often with Dudley for amusement. (Dudley of course was never punished for complicity). Before the age of eight, he had experienced numerous telepathic accidents that had enraged his aunt and uncle and he had been whipped with a belt strap, and then warned sternly never to try that again. But he soon found that he could harness his power, and pretty soon he made sure never to show his abilities in front of his aunt and uncle.
Harry took to searching the libraries both at school and the ones in his neighbourhood searching for an answer to these abilities. In addition to controlled telekinesis, he found he could change the size or shade of colour of anything temporarily, communicate precisely with pet dogs, and even more precisely with snakes that he had encountered on a school trip to the zoo. And if he concentrated very hard he could even teleport short spaces but he found this only worked if there was no one watching him.
He never came close to finding the truth and in his young enthusiastic mind he was convinced that there were super humans with these special abilities hidden from the prejudiced world, and very much looked forward to the day when he could interact with them and join their secret society.
Harry also regularly had to perform chores for his relatives, but it was mostly for things that he found mildly interesting, such as gardening. Anyways the Dursleys were well off enough to hire a maid to clean the house on week-ends. During the summers and Christmas vacations, the Dursleys would always vacation in Majorca while he would be left in the care of Mrs. Figg who always seemed to Harry as if she was hiding something from him, terribly nervous.
Harry was always tall for his age, and although wiry, he often best his own cousin in a fight with his superior agility and reflexes. At school, he was relatively popular even though the sense of his own power and abilities made him feel distinct and superior from the rest of the kids. While he had shown his special powers to them on several occasions to get them to believe his stories, he found that they would always forget it all strangely enough, a few days later. He never dared to tell an adult, given his experience with the Dursleys and he was intelligent enough to realize from the comics he had read, that he would run the risk of being experimented on.
Harry also never received a present in his life. But once per year, either on his birthday or at Christmas, or sometimes on both occasions if he had been growing quickly, the Dursleys would buy him a new set of cheap clothes plus a pair of shoes that fit him reasonably well.
And so on the eve of his eleventh birthday, it appeared that Dumbledore's gamble had indeed paid off and Harry had had the best childhood he could have hoped for under the circumstances, having been neither spoiled due to his celebrity, exalted status, or crushed by the weight of expectations. He had developed a curious and eager desire to further the abilities that were revealed to him through accident, and then experimentation.
And then a letter was delivered to him several weeks before his eleventh birthday. Strangely enough, Harry who was collecting the mail noticed that it had no stamps or address of sender, and a strikingly detailed knowledge of where he slept, the smallest bedroom of the house. Thinking quickly, before he could march back into the kitchen, and knowing that all his letters were always read in advance by Uncle Vernon or Aunt Petunia, he pocketed it for later.