In Harry Potter and the Chamber of Secrets it is written that Harry's wand is locked up with the broom in the cupboard:
All Harry’s spellbooks, his wand, robes, cauldron and top-of-the-range Nimbus Two Thousand broomstick had been locked in a cupboard under the stairs by Uncle Vernon the instant Harry had come home.
Later it is written that Harry
had been on the point of unlocking Hedwig’s cage by magic and sending her to Ron and Hermione with a letter
But how could Harry have opened Hedwig's cage if he didn't have his wand?
Countless times, Harry had been on the point of unlocking Hedwig’s cage by magic and sending her to Ron and Hermione with a letter, but it wasn’t worth the risk. Underage wizards weren’t allowed to use magic outside school. Harry hadn’t told the Dursleys this; he knew it was only their terror that he might turn them all into dung beetles that stopped them locking him in the cupboard under the stairs with his wand and broomstick.