That seems to be it!

It took me a while but I found the voltage reference on the schematic. It is made of discrete components which are marked as R26-28, D8, VR1. D8 is LS-5010HN which is a 1.2V reference. So a measured the voltage across the zener and it is 1,53V! The ratio between 1,2 and 1,53 is 0,784 which is exactly the ratio between the measured voltage and the anticipated actual voltage. This also explains why only the resistance ranges are fine since the reading of resistance is determined by the ratio of test current and measured voltage which both are dependent on the voltage reference (the reading should therefore be independent on the reference voltage, is it not?). On the other hand current and voltage ranges just compare the measured voltage to the reference voltage therefore the reading changes with reference voltage (does it not?).

So that is fantastic. Now there are the questions. Why did the reference voltage change? What could suddenly damage the zener? Is it the zener itself what is damaged or could there be some other causes? (These questions are supposed to be rhetorical to direct the discussion).

So please post your thoughts and conjectures.

Datasheet of LS5010 is attached bellow.