Heater problem

Hi there. I have no heat at all in the front and rear floor heaters in my 99 3L turbo diesel super custom 1KZ-TE engine. I've tried most of the things mentioned in this thread but still no solution.

Simple question: what propels the fluid into the pipes leading to the matrix (assuming this is the heat exchange behind the dash). I have confirmed valve is open wide, flushed those lines (lots of brown water did come out for ages), and also confirmed that when flushing into the pipe between the matrix and valve water comes out the radiator fill point. But when the engine is running and I have the pipe disconnected from the open valve, virtually no water comes out of either end - an initial trickle but then nothing at all. Is there any exchange or other valving in the system?

It seems strange that insufficient warm water reaches the lower rear heater too. Both heaters are dead cold. Could the water pump be working weakly perhaps? No apparent problems with overheating. The temp gauge sits stable at about half constantly.

Thanks for any help you may be able to provide.
Cheers, Owen.

Our '98 Super Custom had a cracked head. I got it replaced but now the climate control air conditioning will only cool. It doesn't heat at all. I took it back to the mechanic but he couldn't find anything. He suggested I check the fuses which I did. Couldn't find anything. Looks like I'm on my own. Any help would be appreciated.