I going to go with an expectation that the noise happens when you turn the key but don't turn the key further to start the engine. There is a common noise that you will hear from the dash of the car that is an ignition relay that will buzz or vibrate if the ignition key is turned too slowly. That could be interpreted as a weird noise that happens sometimes. If you turn the key from the off to the start position quickly you won't hear the noise. If you are slow to turn the key or do so very deliberatly then you will hear the noise. It is a charactoristic of the car and can't be fixed to my knowledge.if the noise happens after you start the car is could be a loose belt or a bad pulley bearing such as an idler pulley or a power steering pump pulley. Both would be very unusual on a 2004 accord but depending on the mileage you may have one or the other. Those noises usually only happen the first time you start the car after the car has been sitting for a longer period of time such as overnight. once the engine is run the lubricant on the pulley bearings warms up and does a better job of absorbing the noise; same with belts that warm up and get a better coefficient of friction when warm.if the screeching noise is only when you first start to back out or pull forward then the cause of the noise would be the wear sensors on the brake pads. That noise is a screeching noise but only happens when the car is moving and you foot is not on the brake. You typically only hear the noise at lower speeds as it is drowned out by the road noise at higher speeds.hope that helps