Why doesn't pure water conduct when it dissociates?
Pure water does conduct as pointed out by the above comments. But it has very less dissociation hence there are very few ions to conduct electricity.
you may have heard that pH of pure water is 7. This statement implies that the concentration of H+ ion is 10^-7. Since it is a neutral solution concentration of OH- ion is also 10^-7. As such the conducting property of water is very less.