locating pump

I have recently drained my central heating system, flushed all the radiators and bled them until water flowed from the valve (because some rads had cold bottoms and warm tops and others cold tops but warm bottoms). This is my first winter in the house and the the first time that I have experienced all the radiators being on: and on this event I have noticed one cold rad downstairs - closest to the boiler (it will warm if those upstairs are turned off).

Having gone though a balancing exercise (to distribute the hot water to the rads efficiently) I have run out of ideas to get warm water to the to the radiator closetst to the boiler - which seems to be the last one in the chain. Does anyone have a good idea for a next step?

"cold bottoms and warm tops "
That means serious corrosion/sludge.
Either
Read up on powerflushing and hire a machine to do it
Take your rads into the garden and shoot mains through them and invert a lot to sort of flush them
With some messing about, use a mains hose connected to say one rad tail with a hose to drain on the other, then close all but one rad, flush till water clear, open second rad, close first, and so on.
Or pay someone £300-£500 to powerflush the system.