You made a good use of the search here.
In case that you do not have hot air when the power plug is connected but hot air when the plug is disconnected, the valves should be o.k. Without power they are full open when they work (spring actuated)
The control module for the IHKA is behind the evaporator, microfilter and sword, close to the firewall. Remove BOTh sides of the cover in the footwell on driver and passenger side. The control module has on each side 2 connectors, which you have to unplug. is has a clip which is open to one side. So pyll it out and disassemble it. resolder all soldering points and
probably you have to replace the capacitors. Alll is nicely described on Johan's page.
http://bmwe32.student.utwente.nl/johan/ihka/ihka.html
What you could check before are the thumbwheels for regulating the temperature and the control panel of the IHKA right under the radio. The valves are controlled by pulses, so if you turn the thumbwheels, the frequencies of the pulses must be higher or lower depending on the setting.
Use a multimeter and check on the plug at the heater valves.
A noisy aux heater pump is not a good sign. Maybe it is on the way out. Will cost you about 120 $, or buy one from a junkyard. The ones from the 5 E34 series will fit too.
The sword is only to control the speed of the blower fan. Not involved in the settings of the temperature.