One would assume that having done all that, the system would work. Some cars will not allow you to remove the thermostat, and if you do will cause you problems, so check this out on your car first. The system is very simple in that the pump should pump, the water goes from the block via the thermostat (and if open) to the top of the rad, through the rad to be cooled and then out of the bottom hose back to the engine block.

You say that the new pump is functioning, and that the rad is not blocked, so if the thermostat is ok then there is very little else left. If push comes to shove you might want to recheck that the pump is working correctly - remove the top hose, start the engine and then water should pump out of the top hose almost immediately. If the thermostat is fitted then you would have to wait until the temperature has risen to allow water to pass it and come to the top of the radiator.