The K-304-KS is a pressure balancing valve. In order for a pressure balancing valve to function correctly, equal pressure must be applied to the hot and cold inlets on the valve. You should have a minimum of 45 psi on both hot and cold.
Verify the stops are open (turning left). The K-304-KS features integrated screwdriver stops that allows the user to turn the water on and off right on the valve. If the stops are closed (turning right), water will not pass through that port.
After checking water pressure and stops, make sure the internal components are installed properly and are not damaged. The Installation Instructions require the removal of the pressure balancing unit and mixer cap prior to soldering the pipes to the valve. If this was not done, the parts may have been damaged.