I just replaced the water valve, It did slow down the dripping. It appears to start dripping a few minutes after getting water.

You may want to check the water supply to see if it is adequate. It is water pressure that actually holds the valve closed, so if the pressure is not adequate, it can drip through and cause headaches for you. I would check to see if your water supply is attached to the water line with a self-piercing valve. These make such a small hole in the line that they get clogged up and cut down on you water volume/pressure. A better alternative is a valve which actually looks the same but to install you drill a 1/4" hole in the line, then strap on the valve. Available in most hardware stores for a couple of bucks.