In the diagram posted, you can easily see how the system works with the manual switch.
Position 0 - there is no ground connection and the blower does not run.
Position 1 - three resistors are connected in series ( the resistance values are added together when in series) so there is maximum resistance, minimum current and the fan runs slowly.
Position 2 - two resistors connected in series so fan runs faster
Position 3 - one resistor in series, fan runs faster still.
Position 4 - no resistors in the circuit so fan runs at maximum.
I've looked on eBay and there are pictures of these resistor blocks and they seem to have 4 connectors and an open cage at the rear, and this opens cage would allow air to flow and cool the resistors.
The chances of having three faulty resistor units are vanishingly small, so the problem is somewhere else.
If it was me, I would take a multimeter set to resistance (ohms) and measure between the 4 pins of the resistance unit.
1-2, 1-3, 1-4 then 2-3, 2-4 and finally 3-4.
Produce a sketch of what you find see how it compares with the posted diagram. It should make sense and be the same.
I don't know how your " screen display" unit works, but it's bound to do something similar to the manual 4 position switch, but the switching will somehow be done electronically.
That is most probably where the issue is.
Electrical fault finding on 12 volt system is mostly about understanding the circuit, measuring voltages and resistances and concluding where the problem must be.